D-band theory

The d-Band Theory of Surface Reactivity and Rationai Approach to Catalyst Design... 

We have seen that the early hope that catalytic studies on Cu-Ni alloys would provide clear confirmation of the simple d-band theory has... 

Gold forms a continuous series of solid solutions with palladium, and there is no evidence for the existence of a miscibility gap. Also, the catalytic properties of the component metals are very different, and for these reasons the Pd-Au alloys have been popular in studies of the electronic factor in catalysis. The well-known paper by Couper and Eley (127) remains the most clearly defined example of a correlation between catalytic activity and the filling of d-band vacancies. The apparent activation energy for the ortho-parahydrogen conversion over Pd-Au wires wras constant on Pd and the Pd-rich alloys, but increased abruptly at 60% Au, at which composition d-band vacancies were considered to be just filled. Subsequently, Eley, with various collaborators, has studied a number of other reactions over the same alloy wires, e.g., formic acid decomposition 128), CO oxidation 129), and N20 decomposition ISO). These results, and the extent to which they support the d-band theory, have been reviewed by Eley (1). We shall confine our attention here to the chemisorption of oxygen and the decomposition of formic acid, winch have been studied on Pd-Au alloy films. 

We have, then, another example of an alloy and reaction in which the simple d-band theory has to be modified in a rather speculative way in order to explain experimental results. Actually, this is unnecessary for the formic acid reaction if we take the more recent value of about 0.4 for the number of d-band holes per palladium atom. This is not a satisfactory solution, because it is then difficult to explain the low activation energy for the parahydrogen conversion on Pd-Au alloys containing between 40 and 60% Pd. 

Much effort has been made to enhance the performance of Pd—M (where M = second metal) for alcohol electrooxidation. These efforts were persuaded by the bifunctional mechanism and the electronic/Ugand effect, which can be explained by either the electron density, electronegativity, density functional theory, or d-band theory [6-17]. For example, according to the bifunctional theory of electrocatalysis, the oxidation of a primary alcohol to CO2 and R-COOH (or and R-COO in... 

The Es on the Pd-Pb/C is more negative than that on the Pd/C. The Pd-Pb (4 1) has a better activity than the Pd/C catalyst. The addition of Pb facilitates the oxidative removal of CO. The promoting effect of Pb is explained by a bifunctional mechanism and d-band theory... 

Pd-Pb/C catalysts with different amounts of Pb were prepared using NaBH4 chemical reduction method in the presence of sodium citrate. Pd-Pb (4 1)/C showed better activity towards ethanol electrooxidation in alkaline electrolyte than Pd/C catalyst. The Arrhenius equation was used to calculate the activation energy, which showed a smaller value, thus implying a faster charge transfer process. The enhanced activity of Pd-Pb/C was explained by a bifunctional mechanism and the d-band theory [56]. Pd4-Au/C and Pd2.5-Sn/C catalysts prepared by He et al. [72] showed lower activity for ethanol electrooxidation in alkaline electrolyte than commercial Pt/C but were more tolerant to poisoning. 

Nprskov and coworkers have successfully developed a d-band theory in relating the adsorption properties of rate-limiting intermediates in catalytic process to electronic structure of catalyst surfaces [44, 45]. According to this theory, the... 

This finding, together with the XRD data for the nanocrystal core properties [58], demonstrated that both the core and the surface of the bimetallic nanopartides exhibit bimetallic alloy properties. The detection of both Au-atop and Pt-atop CO bands on the surface of the alloy nanoparticles of a wide range of bimetallic composition can be correlated with the electronic effect as a result of the d-band shift of Pt in the bimetallic nanocrystals. There exists a stronger electron donation to the CO band by a Pt-atop site surrounded by Au atoms in the bimetallic alloy surface than that from the monometallic Pt surface as a consequence of the upshift in d-band center of Pt atoms surrounded by Au atoms, which explains the preference of Pt-atop CO over the Au-atop CO adsorption. The observed decrease of the Pt-atop CO band frequency with increasing Au concentration is in agreement with the d-band theory for the bimetallic system [172]. 

In the past, d-band theory has been successfully used to explain the reactivity of a wide range of catalysts. It was taken for granted that the participation of the structureless and wide sp band was not relevant. However, we want to emphasize that this approach is an oversimplification that could lead to wrong results. We have included two different pictures of the same system in order to show the behavior of the electron bands during the adsorption process. The electronic properties of a hydrogen atom approaching to the surface of a three palladium atoms cluster on Au(lll) are shown in Figure 1.16. 

A book edited by Levinson (1981) treated grain-boundary phenomena in electroceramics in depth, including the band theory required to explain the effects. It includes a splendid overview of such phenomena in general by W.D. Kingery, whom we have already met in Chapter I, as well as an overview of varistor developments by the originator, Matsuoka. The book marks a major shift in concern by the community of ceramic researchers, away from topics like porcelain (which is discussed in Chapter 9) Kingery played a major role in bringing this about. 

Like Rh and Ir, all three members of this triad have the fee structure predicted by band theory calculations for elements with nearly filled d shells. Also in this region of the periodic table, densities and mps are decreasing with increase in Z across the table thus, although by comparison... 

D.M.Nicholson and J.S.Faulkner, Apphcations of the quadratic Korringa-Kohn-Rostoker band-theory method , Phys.Rev. B39 8187 (1989). 

The mechanism of the poisoning effect of nickel or palladium (and other metal) hydrides may be explained, generally, in terms of the electronic theory of catalysis on transition metals. Hydrogen when forming a hydride phase fills the empty energy levels in the nickel or palladium (or alloys) d band with its Is electron. In consequence the initially d transition metal transforms into an s-p metal and loses its great ability to chemisorb and properly activate catalytically the reactants involved. 

A pure transition metal is best described by the band theory of solids, as introduced in Chapter 10. In this model, the valence s and d electrons form extended bands of orbitals that are delocalized over the entire network of metal atoms. These valence electrons are easily removed, so most elements In the d block react readily to form compounds oxides such as Fc2 O3, sulfides such as ZnS, and mineral salts such as zircon, ZrSi O4. ... 

The same theory, i.e. Eqs. (86) and (87), allows us to understand why CO and similar molecules adsorb so much more strongly on under-coordinated sites, such as steps and defects on surfaces. Since the surface atoms on these sites are missing neighbors they have less overlap and their d band wUl be narrower. Consequently, the d band shifts upwards, leading to a stronger bonding. 

The experimental evidence, first based on spectroscopic studies of coadsorption and later by STM, indicated that there was a good case to be made for transient oxygen states being able to open up a non-activated route for the oxidation of ammonia at Cu(110) and Cu(lll) surfaces. The theory group at the Technische Universiteit Eindhoven considered5 the energies associated with various elementary steps in ammonia oxidation using density functional calculations with a Cu(8,3) cluster as a computational model of the Cu(lll) surface. At a Cu(lll) surface, the barrier for activation is + 344 k.I mol 1, which is insurmountable copper has a nearly full d-band, which makes it difficult for it to accept electrons or to carry out N-H activation. Four steps were considered as possible pathways for the initial activation (dissociation) of ammonia (Table 5.1). 

The rise in activation energy on films occurred at a Ag content slightly higher than the 60% commonly expected from (2-band theory. Various reasons why an exact correspondence should not be expected were discussed, e.g., the possibility of d-s promotion of electrons in Ag and absorption of hydrogen in the Pd-rich alloys. In the case of the Pd-Ag wires, most of the increase in activation energy occurred beyond 80% Ag. The authors of the latter work demonstrated a correlation between the experi-... 

We now look at some results, calculated via the above theory, for a pair of H atoms chemisorbed on several d-band metals (Ti, Cr, Ni, Cu). Corresponding results for III-V and sp-hybrid semiconductor substrates have been given by Schranz and Davison (1998, 2000). 

It is generally believed then that with metals the electronic configuration, in particular the catalytic activity [21], In this theory it is believed that in the absorption of the gas on the metal surface, electrons are donated by the gas to the d-band of the metal, thus filling the fractional deficiencies or holes in the d-band. Obviously, noble metal surfaces are particularly best for catalytic initiation or ignition, as they do not have the surface oxide layer formation discussed in the previous sections. 

Using perturbation theory. Hammer and Nprskov developed a model for predicting molecular adsorption trends on the surfaces of transition metals (HN model). They used density functional theory (DFT) to show that molecular chemisorption energies could be predicted solely by considering interactions of a molecule s HOMO and LUMO with the center of the total d-band density of states (DOS) of the metal.In particular. 

The authors (Sun et al, 1991, 1993c, d, 1994b Hu et al., 2000 Wang et al., 1992) used CNDO/2 method of quantum chemistry and band theory to study the flotation mechanism of sulphide minerals in the presence and absence of collectors. 

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