Ligand effects in heterogeneous catalysis and electrochemistry
Introduction
Modern density functional theory (DFT) calculations provide a method to resolve the electronic structure of even rather complicated model systems with adequate accuracy at a reasonable computational cost [1]. A class of systems for which DFT has been applied with considerable success involve chemical reactions taking place on solid surfaces [2]. Both in heterogeneous catalysis and in electrochemistry it is important to understand the chemical bonding of atoms and molecules to transition metal surfaces. The best transition metal catalyst for a given reaction will to a large extent be determined by the ability of the metal to bond the key reaction intermediates in just the right way [3], [4]. When going through the periodic table, the adsorption properties of the pure metals vary enormously, and it is the changes in the electronic structure of the metallic surface which lead to these variations. An atomic-scale understanding of phenomena in both heterogeneous catalysis and in electrochemistry is therefore intimately tied to an understanding of the electronic structure of the catalyst or electrode surfaces.
Only a small fraction of the research being carried out in the fields of electrochemistry and heterogeneous catalysis is related to electronic structure theory, and this seems to suggest that in both classes of systems large complexities are present which are necessary to take into account in order to actually understand specific reactions. This is perhaps most true for electrochemical reactions, where the complexity of the electrolyte–surface interface with varying ion concentrations and local field effects seems larger than for a gas phase heterogeneous reaction. Some surface catalyzed reactions are understood in elaborate detail both from experiment and from theory. One example is ammonia synthesis [5], which is one of the most studied reactions from the electronic structure point of view [6]. Calculating the reaction rate for a particular catalyst is an enormous task [5], but it turns out that if the goal is to determine which of the elements in the periodic table is the best catalyst, a much simpler approach is sufficient [7]. The reason for this is that the change in electronic structure from one element to the next in the periodic table implies large variations in adsorption and activation energies for the elementary steps of this reaction. In spite of changes in the specific adsorption sites for the intermediates, changes in relative coverages of various intermediates the experimental trends are systematically reproduced by adding only the simplest level of micro-kinetic analysis to the results of the electronic structure calculations [7].
Recently simple models [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19] have been introduced to treat electrochemical systems using DFT calculations, and it has become possible to start performing the same type of trend studies for electrochemical reactions as those that have been known in heterogeneous catalysis. Two cases where trends studies have been initiated are the oxygen reduction reaction [18] and the hydrogen evolution reaction [19]. Whereas the ideas behind such trend studies have been known and used in the field of electrochemistry for half a century [20], the advent of DFT calculations have allowed for the development of systematic databases of adsorption energies. One benefit of this development is that DFT calculations can be used as the basis for the search after new electrode materials [21]. Another benefit is that the entire established apparatus of electronic structure theory now can be applied to the surfaces of electrodes under electrochemical reaction conditions.
In order to understand the variation in adsorption energies that form the basis for describing trends in surface reactivity in both heterogeneous catalysis and electrochemistry it is important to develop simple models or concepts being able to rationalize the data. A particularly useful model in heterogeneous catalysis, which is often used to relate changes in the electronic structure of transition metal surfaces to changes in chemical reactivity is the d-band model [22], and in the following we will review some of the features of this model.
Section snippets
The d-band model
In the d-band model variations in adsorption energies and activation barriers for a given reaction from one transition metal to the next are given, to a first approximation, by variations in the coupling between the adsorbates levels and the transition metal d-bands. The adsorbate–surface bond is viewed as consisting of two contributions:where ΔE0 is the bond energy contribution from the coupling of the adsorbate states to the free-electron-like s-electrons and ΔEd is the contribution
Variations due to changes in surface structure
The d-band center can be varied for a specific transition metal by varying the structure. As mentioned above, the bandwidth depends on the coordination number of the metal and this leads to substantial variations in the d-band centers [24]. The atoms in the most close-packed (1 1 1) surface of Pt have a coordination number of 9. In the more open (1 0 0) surface it is 8 and at a step or at the (1 1 0) surface it is 7. At a kink the coordination number is as low as 6. As shown in Fig. 3, this leads to
Variations due to alloying
Effects due to alloying can also be understood in terms of d-band shifts. This is already evident from Fig. 3. Fig. 5 shows this in more detail. By considering a Pt(1 1 1) surface where a series of different 3d metals have been sandwiched between the first and second layer one can study the effect of second layer atoms on the reactivity of a Pt(1 1 1) overlayer. Such near-surface alloys [35], or “skins” have been extensively studied as oxygen reduction catalysts in PEM fuel cells [36], [37], [38].
Acknowledgments
The authors wish to acknowledge support from the Danish Research Agency through grant 26-04-0047, from the Danish Center for Scientific Computing through grant HDW-1103-06. The Center for Atomic-scale Materials Design is sponsored by the Lundbeck Foundation.
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