Atomic clusters basic properties

An upper limit of cluster size cannot be chosen in any simple or general manner. The basic question, at which size a metal atom cluster may show some or all of the properties of the respective bulk metal, has not been and may not be generally answered, see, e.g. [30]. Nevertheless, there are several assumptions or suggestions of upper limits in the literature n 1000 is used by Friedel [3] and in a review of transition-metal atom clusters by Whetten et al. [31], the latter following a statement of Jortner [6], that at n lO a gradual evolution of a solid-state structure takes place (the size classification was, however, for nonmetallic systems). Somewhat less specific are the limits n about a few hundred [2] or n about a few thousand [30]. An upper limit may also be explicitly defined by the number... 

Electric Properties of Atoms, Molecules, and Clusters. Basic Theory and Computational Aspects... 

Certainly, it would be trivial to point out here the reasons for which small clusters have always attracted considerable attention. Their unusual behavior has proved significant for a number of physical phenomena such as catalysis, adsorption, photography, electrochenrical deposition of metals, semiconductors and alloys etc. Several authors already in the seventies obtained valuable information on the stmcture, the energetics and the thermodynamic properties of the microclusters [1.108-1.113]. This Chapter, however, is not going to discuss the basic achievements in this field. Here we shall provide information on the small clusters behavior obtained by means of illustrative model considerations. For the purpose we shall firstly calculate the nucleation work of 1- to 19-atomic clusters formed on a stmctureless foreign substrate [1.107] (see also [1.67] and [1.114]). 

Substitution at one or more metal sites will generally break the symmetry of the cluster core, and can greatly influence its electronic properties and reactivity. Consider, for example, the possible substitutions of a metal M into an octahedral core of composition MfiX v (x = 8, 12). The first substitution will afford an MsM X core, for which the symmetry has been lowered to C4v. A second substitution generates an M4M 2Xx core with two possible isomers One in which the M atoms are positioned at trans vertices (D4/,) and another where they are positioned at cis vertices (C2v). With a third substitution to give an M3M 3Xx core, fac and mer isomers become possible, while further substitutions simply repeat the pattern with M and M interchanged. Here again, the substitutions can be anticipated to alter the basic electronic properties of the cluster. Moreover, the outer-ligand substitution chemistry could potentially be quite different... 

The cluster calculations for Li+, Na+, and K+ ions in six-membered windows (S,. and Sn sites) were performed by Beran (104). It was concluded that in this series the properties of a zeolite framework (charge distribution, bond orders, Lewis acidity or basicity as characterized by LUMO and HOMO energies) only slightly depend on the type of cation. The decrease of water adsorption heats in this sequence was explained by the assumption that the strength of the water-cation interaction correlates with the strength of the interaction between a cation and lattice oxygen atoms. 

The basic approach of chemical theory to surface science is to model a surface with a cluster of a finite number of atoms, with one or more adsorbate atoms or molecules bonded to various sites on the cluster. In parallel with the chemical theory there is also the solid state physics approach. This starts from an extended surface surface model, where an array of atoms perfectly periodic in two dimensions represents both the substrate and any adsorbates. Many theoretical techniques have been developed for the extended-surface model. We can only refer the interested reader to the literature/87,88,89,90,91,92,93,94/ and remark that the relative merits of the cluster and extended-surface approaches are still very much under active debate. It is clear that certain properties, such as bonding, are very localized in character and are well represented in a cluster. On the other hand, there are properties that have a delocalized nature, such as adsorbate-adsorbate interactions and electrostatic effects, for which an extended surface model is more appropriate. 

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