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First principles studies of the size and shape effects on reactivity of the Se modified Ru nanoparticles

We present here the results of our density-functional-theory-based calculations of the electronic and geometric structures and energetics of Se and O adsorption on Ru 93- and 105-atom nanoparticles. These studies have been inspired by the fact that Se/Ru nanoparticles are considered promising electrocatalysts for the oxygen reduction reaction (ORR) on the direct methanol fuel cell cathodes and the oxygen binding energy is a descriptor for the catalyst activity towards this reaction. We find the character of chemical bonding of Se on a flat nanoparticle facet to be ionic, similar to that obtained earlier for the Se/Ru(0001) surface, while in the case of a low coordinated Ru configuration there is an indication of some covalent contribution to the bonding leading to an increase in Se binding energy. Se and O co-adsorbed on the flat facet, both accept electronic charge from Ru, whereas the adsorption on low-coordinated sites causes more complicated valence charge redistribution. The Se modification of the Ru particles leads to weakening of the oxygen bonding to the particle. However, overall, O binding energies are found to be higher for the particles than for Se/Ru(0001). High reactivity of the Se/Ru nanoparticles found in this work is not favorable for ORR. We thus expect that larger particles with well-developed flat facets are more efficient ORR catalysts than small nanoparticles with a large fraction of under-coordinated adsorption sites.


Introduction
The proton exchange membrane fuel cells (PEMFC) and the direct methanol fuel cells (DMFC), as clean renewable sources of energy, can offer great advantages for various applications. However, the Pt-based catalysts, used in both electrodes of the fuel cell, make these devices unacceptably expensive. Furthermore, performance of both PEMFC and DMFC suffers from low rate of the oxygen reduction reaction (ORR) on the Pt (or Pt-based) cathode. This is thus not surprising that a significant effort has been made in search for new cost-effective Pt-free materials that efficiently catalyze ORR.
One of the focuses of the search is on the Se-Ru system. It has been more than two decades since Alonso-Vante and Tributsch reported a relatively high ORR rate for Mo 4.2 Ru 1.8 Se 8 [1]. More recent studies show that the best electrocatalytic performance is achieved with the Ru x Se y nanoparticles [2][3][4][5][6][7][8][9][10][11]. The main conclusions drawn from these works are that: a) the best catalytic activity is achieved for the few nanometer particles with the Ru core covered with Se at composition Ru 85 Se 15 , b) The Ru core has the bulk-like hcp structure, c) it is not clear how Se is distributed over the particle surface. Recent calculations [12] show that Se adsorbates with submonolayer coverage accept electronic charge from Ru and, therefore, repel each other. The experimental data on the electro-chemical nuclear magnetic resonance and X-ray photoelectron spectra also suggest the electron charge transfer from Ru to Se [13]. As a result, Se atoms tend to scatter over the surface rather than from 2D islands or 3D structures [12,14].
The Se/Ru structures have very promising electrocatalytic properties including: a) relatively high ORR rate, b) excellent tolerance to methanol oxidation, c) high selectivity of fourelectron oxygen reduction to water (small fraction of H 2 O 2 ), and d) high stability towards oxidation. These catalysts are extensively studied [15], however, further progress in this direction requires deeper understanding the factors controlling the ORR energetics on Se/Ru. For example, the mentioned above calculations [12] have been performed for the Ru(0001) surface. This is the lowest energy surface for the hcp structure. One can thus assume that in the large enough particles the (0001) facets will dominate. However, the nano-size effects on the Se distribution over the Ru core have still to be understood. Furthermore, for many materials, the binding energies of OOH (E B (OOH)) and OH (E B (OH)) are found to be approximately proportional to binding energy of atomic oxygen (E B (O)) [17 -20].
Therefore, E B (O) can be used as an ORR descriptor for preliminary screening of materials. It has also been shown that Ru(0001) surface is too reactive (E B (O) is too high) to efficiently catalyze ORR [21]. One thus can expect that the Se modification reduces E B (O) on the Ru surface. The strength of covalent Ometal bond is usually associated with hybridization of oxygen and metal states, which has been shown to depend on the metal d-band center position [22]. The E B (O) -dband center correlation has been reported for various materials including the ORR catalysts [18,23,24]. It is important to note, however, that the Se modification does not change noticeably the density of d-electronic states of Ru surface atoms [12], suggesting that alternative mechanisms of the Se effect on the Ru surface reactivity have to be explored. It has been shown recently [25] that both Se and O accept electronic charge from Ru upon adsorption and, hence, repel each other. This repulsion increases total energy of the system and thus leads to decrease in the O binding energy. However, again, these results were obtained for a selenium modified Ru(0001) surface, and it still needs to be understood how geometry of small Se/Ru nanoparticles affects this mechanism.
In the present work we address the questions raised above. We obtain from first

Computational details
In this work we study the Se/Ru particles with 105 Ru atom core. Some calculations were also performed for a 93 Ru atom particle with relatively large facets.
All calculations in this work have been performed using the VASP5.2 code [26] with projector augmented wave potentials [27] and the Perdew -Burke -Ernzerhof (PBE) version of the generalized gradient approximation (GGA) for the exchange and correlation functional [28].
To maintain periodicity, the particles were situated in a cubic vacuum box of 24 Å side.
Since no dispersion of the electronic states occurs in such systems, the calculations were performed only for Γ point of the Brillouin zone, as it usually done for non-periodic systems modeled by a periodic computational method. The cut of energies of 400 eV and 600 eV were used for the plane wave expansion of wave functions and charge density, respectively. To achieve structural relaxation, the atomic positions were optimized to obtain equilibrium geometric structures in which forces acting on atoms do not exceed 0.02 eV/Å. The binding energy of the adsorbate X (X = O, Se) on a Ru particle was calculated as: Similarly the formation energy per adsorbate, when more than one X atom is adsorbed on the cluster, was defined as: where n is the number of X atoms adsorbed on the surface. These energies are thus positive if adsorption is favorable. Since there are various non-equivalent adsorbtion sites on the Ru core, the formation energy per adsorbate characterizes the average binding energy of the adsorbate on the core.
The valence electron charge redistribution upon O and/or Se adsorption was defined as follows: Geometric structures of the system under consideration and two-dimensional cuts of δρ(r) shown in this article have been plotted using the Xcrysden software [29].

Results and Discussion
First we calculated the optimized geometry of the 105 atom Ru core. The initial shape of the cluster was chosen as a piece of the hcp bulk Ru.
To avoid an unphysical force cancelation due to symmetry of the system, we have randomly deviated atoms from the equilibrium by 0.02 Å. The relaxed Ru core cluster is found to retain an hcp-like structure, although the optimization changes some bond length noticeably. It is important for our further studies that the chosen core cluster has various under-coordinated Ru sites which represent typical geometry of small nanoparticles (see Fig. 1). As seen from Fig. 1, the binding energy of Ru atoms to the cluster depends on local geometry and, in particular, on coordination numbers. Nevertheless, all surface Ru atoms are found to bind to the cluster strong enough to ensure its stability.

Energetics of formation of Se/Ru core-shell structures
In order to understand the mechanism underlying formation of the Se shell on the Ru core, we obtained the optimized geometries, electronic structures and Se formation energies for three Se/Ru structures (see Fig. 2

Oxygen adsorption on the Se/Ru nanoparticle
Since our goal is to evaluate the nanoparticle size and shape effects on ORR on the Se/Ru system, and the oxygen binding energy is considered to be an ORR activity descriptor [16,17], we calculate E b (O) for a number of non-equivalent adsorption sites on the clean Ru 105 atom core and that pre-adsorbed with 18 Se atoms (see Fig. 6) that corresponds to about 30% Se coverage. The calculation results are listed in the Table 1  As seen from the Table 1, presence [25], which is smaller than E b (O) obtained for most sites on the particle. As concluded in Ref. 25, reactivity of the Se/Ru(0001) surface is still higher than optimal one for ORR. We find here that the considered Se/Ru particle with a significant number of under-coordinated Ru sites is even more reactive than Se/Ru(0001). This finding suggests that large Se/Ru nanoparticles with welldeveloped flat facets are more favorable for ORR than small Se/Ru clusters.
In order to trace the obtained Se effect on E b (O) to the electronic structure of the system, first, we come back to   7b). The apex with the lowest Ru coordination in the particle considered here provides the "extreme" geometry for Se and O bonding. One thus may expect that, for more compact configurations, the Se -Ru and O -Ru bonding are more similar to that obtained for the flat facet.

Conclusions
We have performed DFT-based calculations of the electronic and geometric structures and energetics of the Se and O adsorption on the Ru 105-and 93-atom clusters. The lowcoordinated Ru-sites in the clusters are found to be more reactive than those in flat facets.      shows the projection of the cut plane for δρ(r).