The d-band model

In density functional theory the total energy is usually written as  

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These systems represent bonding to surfaces where the adsorbate atoms have unpaired electrons available for covalent interaction with unsaturated electronic states on the metal surface. We denote this bonding mechanism as radical adsorption where the open-shell electrons on the adsorbate atom can form electron pairs with the metal atoms at the surface. These radical atoms have in most cases been obtained through the dissociation of molecules on the surface. Let us make a simple picture of the electronic structure when a simple atomic adsorbate interacts with a transition metal, denoted the d-band model [31,32]. A similar description can also be found in Chapter 4. 

One of the basic assumptions of the d band model is that E0 is independent of the metal. This is not a rigorous approximation. It will for instance fail when metal particles get small enough that the sp levels do not form a continuous (on the scale of the metal-adsorbate coupling strength) spectrum. It will also fail for metals where the d-states do not contribute to the bonding at all. The other basic assumption is that we can estimate the d contribution as the non-self-consistent one-electron energy change as derived above ... 

As a first example of the use of the d band model, consider the trends in dissociative chemisorption energies for atomic oxygen on a series of 4d transition metals (Figure 4.6). Both experiment and DFT calculations show that the bonding becomes... 

The d band model, including Pauli repulsion, can therefore be used to understand variations in oxygen binding energies in the periodic table. It turns out that a similar description can be used for a number of other adsorbates [4,18]. 

Pt surfaces tend to restructure into overlayers with an even higher density of Pt atoms than the close-packed (111) surface [21]. The Pt atoms are closer to each other on the reconstructed surfaces than in the (111) surface. The overlap matrix elements and hence the bandwidth are therefore larger, the d bands are lower and consequently these reconstructed surfaces bind CO even weaker than the (111) surface. The reconstructed Pt surfaces are examples of strained overlayers. The effect of strain can be studied theoretically by simply straining a slab. Examples of continuous changes in the d band center and in the stability of adsorbed CO due to strain are included in Figure 4.10. The effect due to variations in the number of layers of a thin film of one metal on another can also be described in the d band model [22,23]. 

For atomic chemisorption, similar structural effects are found (see the middle panel of Figure 4.10). As for molecular chemisorption, low-coordinated atoms at steps bind adsorbates stronger and have lower barriers for dissociation than surfaces with high coordination numbers and lower d band centers. The d band model thus explains the many observations that steps form stronger chemisorption bonds than flat surfaces [1,20,24-28]. The finding that the correlation with the d band center is independent of the adsorbate illustrates the generality of the d band model. 

While the interpolation model is far from perfect it gives a fast way of estimating the adsorption energies for alloys. Given the simplicity of the model it is surprising how well it works. The d band model can be used to indicate why this is the case. 

The arguments behind the d band model are quite general and should apply to the interactions in the transition state as well as in the initial and final (adsorbed) states of the process. We therefore expect correlations between the d band center and transition state energies to be the same as for chemisorption energies. This is illustrated in the bottom panel of Figure 4.10. Figure 4.16 shows in detail how the activation energy for methane on different Ni surfaces scales with the center of the d bands projected onto the appropriate metal states to which the transition state couples. 

Figure 4.16 also illustrates a case where the indirect interaction of one adsorbate with another can be described by the d band model (the effects of pre-adsorbed C atoms). If two adsorbates interact with the same metal atom, they are often found... 

Figure 4.16 also shows that there are additional effects due to direct interactions between adsorbates that are not described using the d band model. A large adsorbate like S, will have a sizable overlap to the valence orbitals of the incoming molecule, giving rise to a repulsion which is larger than what can be readily explained by the indirect interaction through d band shifts. 

We note that other systems not resembling the simple diatomic molecules considered here may follow a different relationship [86]. There may be other classes of reactions, dehydrogenation or —C bond breaking that may follow other similar relationships and thus form another universality class. We also note that there are exceptions to the relations, most notably for H2 dissociation on near-surface alloys [87]. These deviations from the rules are still describable within the d band model, though [87]. 

Figure 6.16. Illustration of the d-band model governing surface chemical bonding on transition metal surfaces. As the d-band center of a catalytic surface shifts downward more antibonding orbitals become occupied and the surface bond energy of an adsorbate (here an oxygen atom) decreases. An upward shift in the d-band center predicts strengthening of the surface bond.

To evaluate whether trends in chemisorption energies on Pt nanoparticles are consistent with the d-band model, d-band densities of states were projected out for different adsorption sites to determine the corresponding d-band centers relative to the Fermi level. No correlation was observed between the adsorption energies and site-specific d-band centers. Even though metal nanoparticles possess a continuous electronic band structure and, thus, metal-like electronic properties, their catalytic surface properties are not controlled by band structure effects but by the local electronic structure of the adsorption sites. An important conclusion from this study is that... 

Pettersson L, Nilsson A (2014) A molecular perspective on the d-band model synergy between experiment and theory. Top Catal 57(l-4) 2-13. doi 10.1007/sl 1244-013-0157-4... 

Irons. A p contributes the most to the bond strength hence, it is large and negative, whereas AE is a smaller contribution to the bond strength. This is the d-band model... 

Yet another way of changing the d-band center in a controlled way is by alloying. The formation of surface alloys can induce changes in the electronic structure, which can be understood in terms of the d-band model given that the electronic stracture changes are very localized and that the adsorption site remains unchanged. 

Xin H, Linic S. Exceptions to the d-band model of chemisorption on metal surfaces The dominant role of repulsion between adsorbate states and metal [Pg.137]

Schematic density of states (DOS) illustration of the d-band model. The interaction of an adsorbate state with a transition metal can be thought of as a two-step process. The interaction with the broad j-band leads to a broadening and downshift of the adsorbate states. The adsorbate states split into bonding and anti-bonding states upon interaction with the narrow transition metal d-band. Anti-bonding states that are above the Fermi level remain empty and do not weaken the chemisorption.

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