Metal clusters geometrical models

With respect to the thermodynamic stability of metal clusters, there is a plethora of results which support the spherical Jellium model for the alkalis as well as for other metals, like copper. This appears to be the case for cluster reactivity, at least for etching reactions, where electronic structure dominates reactivity and minor anomalies are attributable to geometric influence. These cases, however, illustrate a situation where significant addition or diminution of valence electron density occurs via loss or gain of metal atoms. A small molecule, like carbon monoxide,... 

The story begins in this chapter with the clusters of simplest geometric and electronic structure. These are clusters of p-block elements with defined stoichiometry and structure in which the cluster surface-atom valences are terminated with ligands. The large number known provide the factual base from which clever people have derived models that connect atomic composition with structure. In turn, these p-block models provide a foundation on which to build an understanding of more complex clusters such as condensed clusters, bare clusters and transition-metal clusters. A more comprehensive account of the structural chemistry will be found in older books and reviews, a selection of which will be found in the reading list at the end of each chapter. 

Recent years there have been a considerable interest in studying of binary catalytic systems based on stabilized nanocomposites and amorphous alloys of copper with other metals. The reason is that the catalytic activity of such systems in many cases is sufficiently higher than that of individual metals. The most convenient model for theoretical description of binary systems characterized by the absence of far order is a cluster model. However, quantum-chemical study of binary clusters comprises the significantly more c omplicated problem than that o f individual metals, b ecause a correct theoretical description of metal-another metal cluster systems requires that the used method should be in a position to provide good results of calculations of geometrical, electron stmctures and energetic characteristics of both of individual metals. 

After the brief introduction to the modem methods of ab initio quantum chemistry, we will discuss specific applications. First of all, we will discuss some general aspects of the adsorption of atoms and molecules on electrochemical surfaces, including a discussion of the two different types of geometrical models that may be used to study surfaces, i. e. clusters and slabs, and how to model the effect of the electrode potential in an ab initio calculation. As a first application, the adsorption of halogens and halides on metal surfaces, a problem very central to interfacial electrochemistry, will be dealt with, followed by a section on the ab initio quantum chemical description of the adsorption of a paradigmatic probe molecule in both interfacial electrochemistry and surface science, namely carbon monoxide. Next we will discuss in detail an issue uniquely specific to electrochemistry, namely the effect of the electric field, i. e. the variable electrode potential, on the adsorption energy and vibrational properties of chemisorbed atoms and molecules. The potential-dependent adsorption of carbon monoxide will be discussed in a separate section, as this is a much studied system both in experimental electrochemistry and ab initio quantum electrochemistry. The interaction of water and water dissociation products with metal surfaces will be the next topic of interest. Finally, as a last... 

The alert reader will have realized that almost all examples given in this chapter are from Na. Of course this was on purpose two of the most important conditions to be fulfilled for the excellent validity of the jellium model, namely (a) that the pseudopotential is local and (b) that the geometrical parts of the ionic arrangement are weak, are best met in NaA. In trying other elements we found only one other material that works comparably well — potassium. But the important point to note is that this simple model serves as a guideline for more complex cases. After electronic shells and plasmons have been found in Na, they have been found in almost all metal clusters. In order to get the same quantitative agreement as in the case of Na one has either to do all-electron calculations or to use non-local pseudopotentials, as has been done in the case of Li [39, 40]. But in these... 

From the theoretical standpoint the above issues are addressed by quantum chemistry. On the basis of calculations of various cluster models [191] the properties of surfaces of solid body are being studied as well as issues dealing with interaction of gas with the surface of adsorbent. However, fairly good results have been obtained in this area only to calculate adsorption on metals. The necessity to account for more complex structure of the adsorption value as well as availability of various functional groups on the surface of adsorbent in case of adsorption on semiconductors geometrically complicates such calculations. 

A metal surface that is uniformly flat offers no sites for further growth. In this case a new nucleus, or center of growth, must be formed. Since small clusters of metal atoms consist mainly of surface atoms, they have a high energy content, and their formation requires an extra energy. The basic principles of the formation of new nuclei can be understood within a simple model. We consider a small three-dimensional cluster of metal atoms on a flat surface of the same material, and suppose that the cluster keeps its geometrical shape while it is growing. A cluster of N atoms has a surface area of ... 

The underlying motivation of the work presented in this paper is to provide a theoretical understanding of basic physical and chemical properties and processes of relevance in photoelectrochemical devices based on nanostructured transition metal oxides. In this context, fundamental problems concerning the binding of adsorbed molecules to complex surfaces, electron transfer between adsorbate and solid, effects of intercalated ions and defects on electronic and geometric structure, etc., must be addressed, as well as methodological aspects, such as efficiency and reliability of different computational schemes, cluster models versus periodic ones, etc.. 

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