Metal clusters electronic model

Small metal clusters are also of interest because of their importance in catalysis. Despite the fact that small clusters should consist of mostly surface atoms, measurement of the photon ionization threshold for Hg clusters suggest that a transition from van der Waals to metallic properties occurs in the range of 20-70 atoms per cluster [88] and near-bulk magnetic properties are expected for Ni, Pd, and Pt clusters of only 13 atoms [89] Theoretical calculations on Sin and other semiconductors predict that the stmcture reflects the bulk lattice for 1000 atoms but the bulk electronic wave functions are not obtained [90]. Bartell and co-workers [91] study beams of molecular clusters with electron dirfraction and molecular dynamics simulations and find new phases not observed in the bulk. Bulk models appear to be valid for their clusters of several thousand atoms (see Section IX-3). 

Cl.1.3.1 SIMPLE METAL CLUSTERS AND THE ELECTRON SHELL MODEL... 

The spherical shell model can only account for tire major shell closings. For open shell clusters, ellipsoidal distortions occur [47], leading to subshell closings which account for the fine stmctures in figure C1.1.2(a ). The electron shell model is one of tire most successful models emerging from cluster physics. The electron shell effects are observed in many physical properties of tire simple metal clusters, including tlieir ionization potentials, electron affinities, polarizabilities and collective excitations [34]. 

The metal cluster will be modeled as an infinitely deep spherical potential well with the represented by an infinitely high spherical barrier. Let us place this barrier in the center of the spherical cluster to simplify the calculations. The simple Schrodinger equation, containing only the interaction of the electrons with the static potential and the kinetic energy term and neglecting any electron-electron interaction, can then be solved analytically, the solutions for the radial wave functions being linear combinations of spherical Bessel and Neumann functions. 

Such a simple model, without the barrier due to the Qo at the center, has been used to calculate the electronic shell structure of pure alkali metal clusters[9]. 

The recent interest in the exploration of electrocatalytic phenomena from first principles can be traced to the early cluster calculations of Anderson [1990] and Anderson and Debnath [1983]. These studies considered the interaction of adsorbates with model metal clusters and related the potential to the electronegativity determined as the average of the ionization potential and electron affinity—quantities that are easily obtained from molecular orbital calculations. In some iterations of this model, changes in reaction chemistry induced by the electrochemical environment... 

Pacchioni G, Illas F. 2003. Electronic structure and chemisorption properties of supported metal clusters model calculations. In Wieckowski A, Savinova ER, Vayenas CG. editors. Catalysis and Electrocatalysis at Nanoparticle Surfaces. New York Marcel Dekker. 

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

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,... 

Electronic structural model. The size selective reactivity of these metal clusters Ts surprisi ng. Certainly the metal cluster are... 

The series Structure and Bonding publishes critical reviews on topics of research concerned with chemical structure and bonding. The scope of the series spans the entire Periodic Table and addresses structure and bonding issues associated with all of the elements. It also focuses attention on new and developing areas of modem structural and theoretical chemistry such as nanostructures, molecular electronics, designed molecular solids, surfaces, metal clusters and supramolecular structures. Physical and spectroscopic techniques used to determine, examine and model structures fall within the purview of Structure and Bonding to the extent that the focus... 

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