Metallic clusters theory

S. Ihmaine, C. Perrin, M. Sergent - Croatica Chem. Acta, special issue on Metal Cluster -Theory and Experiment, 68 (4) (1995) 877... 

Stone, A.J. A new approach to bonding in transition-metal clusters. Theory. Mol. Phys. 41, 1339 (1980)... 

Much of the work done on metal clusters has been focused on the transition from cluster properties to bulk properties as the clusters become larger, e.g. the transition from quantum chemistry to band theory [127]. 

Allen GC, Warren KD (1974) The Electronic Spectra of the Hexafluoro Complexes of the Second and Third Transition Series. 19 105-165 Alonso JA, Baibas LC (1993) Hardness of Metallic Clusters. 80 229-258 Alonso JA, Baibas LC (1987) Simple Density Functional Theory of the Electronegativity and Other Related Properties of Atoms and Ions. 66 41-78 Andersson LA, Dawson JH (1991) EXAFS Spectroscopy of Heme-Containing Oxygenases and Peroxidases. 74 1-40 Antanaitis BC, see Doi K (1988) 70 1-26... 

Much remains to be done to develop the chemistry of organic hgands on supported metal clusters, and substantial progress is to be expected as the samples are well suited to characterization, by IR, NMR, and neutron scattering (F. Li, J. Eckert, and B.C. Gates, unpubhshed results) spectroscopies, as well as density functional theory. 

Linear Absorption of Embedded Metal Clusters The Mie Theory... 

In this Section we want to present one of the fingerprints of noble-metal cluster formation, that is the development of a well-defined absorption band in the visible or near UV spectrum which is called the surface plasma resonance (SPR) absorption. SPR is typical of s-type metals like noble and alkali metals and it is due to a collective excitation of the delocalized conduction electrons confined within the cluster volume [15]. The theory developed by G. Mie in 1908 [22], for spherical non-interacting nanoparticles of radius R embedded in a non-absorbing medium with dielectric constant s i (i.e. with a refractive index n = Sm ) gives the extinction cross-section a(o),R) in the dipolar approximation as ... 

Although there are a lot of publications on the chemistry of technetium [2-4] and transition-metal clusters [1,5-8], the chemistry of technetium clusters was insufficiently studied until the early eighties [1,2]. Nevertheless, the available scanty data on the compounds with Tc-Tc bonds inspired hope that interesting results would be obtained in the chemistry of technetium in general, in radiochemistry, and in the chemistry of transition-metal cluster compounds. The anticipated results were actually obtained [9-15] and the conclusion was drawn that technetium had a number of anomalous cluster-forming properties [9]. This review looks at the detailed studies of these properties and their interpretation in terms of electronic structure theory. 

Gas phase transition metal cluster chemistry lies along critical connecting paths between different fields of chemistry and physics. For example, from the physicist s point of view, studies of clusters as they grow into metals will present new tests of the theory of metals. Questions like How itinerant are the bonding electrons in these systems and Is there a metal to non-metal phase transition as a function of size are frequently addressed. On the other hand from a chemist point of view very similar questions are asked but using different terminology How localized is the surface chemical bond and What is the difference between surface chemistry and small cluster chemistry Cluster science is filling the void between these different perspectives with a new set of materials and measurements of physical and chemical properties. 

Theory has participated in all aspects of this area s development. The almost hand-waving arguments used to rationalize their chemical behavior need testing and will likely be replaced by more elegant quantitative discussions. The theoretical aspects( 77 ) and most physical property measurements(78) of small metal clusters have been recently reviewed. 

The information available is discussed in light of the effects of excitation energy and the environment on the photofragmentation process of several transition metal cluster complexes. The photochemical information provides a data base directly relevant to electronic structure theories currently used to understand and predict properties of transition metal complexes (1,18,19). 

Metal clusters in metal oxide systems have not been well-characterized or abundantly investigated up to the present time. Only isolated examples of metal-metal bonded units in oxide lattices have appeared from time to time. It will be the thesis of this presentation to show that highly unusual structures determined by strong metal-metal bonding will be found in ternary and quaternary metal oxide systems, and that opportunities abound for creative work on the synthesis, theory and structure-property relationships of such compounds. Because of the well-known correlation of d-electron population and d-orbital radial extension with metal-metal bond formation,... 

Theory for the Size and Structural Dependendence of the Ionization and Cohesive Energy of Transtion Metal Clusters. 

This article provides an overview of the information which can be obtained by X-ray absOTption spectroscopy, with emphasis on the utilization of this technique to chari terize the metal clusters in proteins. No attempt is made to provide a detailed description of either the theory or the practice of X-ray spectroscopy these topics have been discussed in a number of excellent review articles (1). Rather, a small sample of the recent literature is used to illustrate both the potentials and the limitations of the... 

The accurate quantum mechanical first-principles description of all interactions within a transition-metal cluster represented as a collection of electrons and atomic nuclei is a prerequisite for understanding and predicting such properties. The standard semi-classical theory of the quantum mechanics of electrons and atomic nuclei interacting via electromagnetic waves, i.e., described by Maxwell electrodynamics, turns out to be the theory sufficient to describe all such interactions (21). In semi-classical theory, the motion of the elementary particles of chemistry, i.e., of electrons and nuclei, is described quantum mechanically, while their electromagnetic interactions are described by classical electric and magnetic fields, E and B, often represented in terms of the non-redundant four components of the 4-potential, namely the scalar potential and the vector potential A. 

In this review we shall first establish the theoretical foundations of the semi-classical theory that eventually lead to the formulation of the Breit-Pauli Hamiltonian. The latter is an approximation suited to make the connection to phenomenological model Hamiltonians like the Heisenberg Hamiltonian for the description of electronic spin-spin interactions. The complete derivations have been given in detail in Ref. (21), but turn out to be very involved and are thus scattered over many pages in Ref. (21). For this reason, we aim here at a summary that is as brief and concise as possible so that all relevant connections between different levels of approximation are evident. This allows us to connect present-day quantum chemical methods to phenomenological Hamiltonians and hence to establish and review the current status of these first-principles methods applied to transition-metal clusters. 

An important consequence of the nonutilization of tangential orbitals is that platinum clusters often do not obey the normal electron counting rules and appear to be electron deficient (19,21,29,58,75,76). Electron counts are usually intermediate between those found in normal transition metal clusters (58-68) and those observed in gold clusters (58,78), but no satisfactory general electron counting theory has been developed for Pt-containing clusters. In small Pt clusters constructed from PtL2 units, theoretical studies have shown that the total electron count depends on the relative orientation of the... 

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