Shell Model metal oxides

G. Metal Cluster and Metal Oxide Anion Reactions Cluster Reactivities Reactivities and the Electronic Shell Model... 

If the initiation step, the activation of H2, is fast, as may be the case on noble metal oxides or highly defective oxide surfaces, the shrinking core or contracting sphere model applies (see Figure 2.3). The essence of this model is that nuclei of reduced metal atoms form rapidly over the entire surface of the particle and grow into a shell of reduced metal. Further reduction is limited by the transport of lattice oxygen out of the particle. The extent of reduction increases rapidly initially, but slows down as the metal shell grows. 

For supported metal and metal oxide systems, one typically has to resort to using two different QM methods owing to the lack of accurate force fields or empirical potentials to describe these systems. Both Whitten and Yangl l and Govind et al.1 1 have developed schemes which embed more accurate Cl wavefunction methods into lower level QM methods in order to provide for more accurate descriptions than DFT. Sauer s group has used standard ab initio methods along with shell models to describe the oxide environment for zeolite systemsl 1. 

Potentials that treat the polarization and ionization are important for modeling a number of metal oxide systems. This is difficult since polarization in solids is a many-body effect with various components and depends strongly upon changes in the electronic structure as a function of structure and forces on the ions. One of the most widely used approaches to simulate polarizability effects is that of the Shell model which uses a massless shell of charge (electron density) I 1. 

The first step in the reduction process, after removal of a layer of chemisorbed water at ca 400 K, is the dehydration and partial reduction of the rust layer. This leads to the formation of a surface containing ferric and ferrous ions, together with structural promoters in the form of pure binary oxides which are dissolved in spinel structures. This step also opens up some of the cracks and pores. Eventually, wustite which initially could not be found on any of the outer surfaces is reduced to iron, and this further increases the voids between the magnetite particles. This step of widening of the cracks and defects, which can be seen only indirectly by photoelectron spectroscopy (e.g., by the induction period found in the UPS experiments), is crucial for the subsequent reduction of the bulk magnetite. This is because it is known that the reduction occurs only along such defects, which provide the sites for heterogeneous nucleation of metallic iron. This led to the core and shell model of activation described in Section 2.5. 

The disorder in the electron shells is to be comprehended in an analogous manner. Here the bonding electrons, more precisely the valence electrons, have left their regular positions and have been excited into the conduction band. This also creates excess particles and missing particles, which are conduction electrons (e ) and electron holes (h ). Let us take a metal oxide with the (perfect) composition MO as our model compound and for the purpose of better visualization assume that, to a good approximation, the valence band is composed of the oxygen p-orbitals, while the conduction band is composed of the outer metal orbitals. Hence, the reaction can also be formulated as an internal redox reaction... 

In low oxidation states, transition metals possess filled or partly filled d shells. The Dewar-Chatt-Duncanson model envisages some of that electron density in (local) d (e.g. d., d y) orbitals being donated into the empty n orbitals of the carbon monoxide ... 

The main handicap of MD is the knowledge of the function [/( ). There are some systems where reliable approximations to the true (7( r, ) are available. This is, for example, the case of ionic oxides. (7( rJ) is in such a case made of coulombic (pairwise) interactions and short-range terms. A second example is a closed-shell molecular system. In this case the interaction potentials are separated into intraatomic and interatomic parts. A third type of physical system for which suitable approaches to [/( r, ) exist are the transition metals and their alloys. To this class of models belong the glue model and the embedded atom method. Systems where chemical bonds of molecules are broken or created are much more difficult to describe, since the only way to get a proper description of a reaction all the way between reactant and products would be to solve the quantum-mechanical problem at each step of the reaction. 

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