Metal clusters energy states

Accepting that the electronic structure of the metal clusters is in between the discreet electronic levels of the isolated atoms and the band structure of the metals, it is expectable that under a certain size the particle becomes nonmetallic. Indeed, theoretical estimations [102,105] suggest that the gap between the filled and empty electron states becomes comparable with the energy of the thermal excitations in clusters smaller than 50-100 atoms or 1 nm in size, where the particles start to behave as insulators. A... 

A. G. Zacarias, M. Castro, J. M. Tour, J. M. Seminario, Lowest Energy States of Small Pd Clusters Using Density Functional Theory and Standard ab Initio Methods. A Route to Understanding Metallic Nanoprobes, J. Rhys. Chem. A. 1999,103,7692-7700. 

A knowledge of these enthalpic terms, and therefore of the relative bond energies, would be expected to considerably clarify many of these fundamental aspects. The data in Table 4 show that, with the main exception of rhenium and osmium, the metal-metal distances in the tetranuclear clusters and in the pure metals are quite similar this relationship is generally valid for all the polynuclear carbonyls60. The metal-metal bond energies in clusters are therefore expected to be of the same order as those in the metallic state for a close-packed arrangement, these are given by the formula Z m-m = A//f M(g)/6. 

Fig. 1 The effect of size on metals. Whereas bulk metal and metal nanoparticles have a continuous band of energy levels, the limited number of atoms in metal clusters results in discrete energy levels, allowing interaction with light by electronic transitions between energy levels. Metal clusters bridge the gap between single atoms and nanoparticles. Even though in the figure the energy levels are denoted as singlets, we must remark that the spin state of the silver clusters is not yet firmly established...

On the practical side, we note that nature provides a number of extended systems like solid metals [29, 30], metal clusters [31], and semiconductors [30, 32]. These systems have much in common with the uniform electron gas, and their ground-state properties (lattice constants [29, 30, 32], bulk moduli [29, 30, 32], cohesive energies [29], surface energies [30, 31], etc.) are typically described much better by functionals (including even LSD) which have the right uniform density limit than by those that do not. There is no sharp boundary between quantum chemistry and condensed matter physics. A good density functional should describe all the continuous gradations between localized and delocalized electron densities, and all the combinations of both (such as a molecule bound to a metal surface a situation important for catalysis). 

Electron-electron collisions induce further thermalization and transport excitation energy from the 1 ph modes to 2ph and higher configurations. The collision rate is however much suppressed at low excitation energies due to Pauli blocking of the final scattering states. The relaxation times from these electron-electron collisions thus strongly depend on cluster s temperature. The evaluation of these times in metal clusters is not yet. standard. We rely here on a first attempt, in this direction, performed at a semi-classical level... 

We discuss here two examples of vibronic effects in polynuclear highly symmetrical transition metal clusters. The existence of degenerate and quasi-degenerate molecular orbitals in their energy spectra results in the Jahn-Teller effect or in the vibronic mixing of different electronic states. We show that both quantum-chemical methods and model approaches can provide valuable information about these vibronic effects. In the case of the hexanuclear rhenium tri-anion, the Jahn-Teller effect is responsible for the experimentally observed tetragonal distortion of the cluster. The vibronic model of mixed-valence compounds allows to explain the nature of a transient in the photo-catalytic reaction of the decatungstate cluster. 

In the 3d metal-cluster SMM cases, where energy separations between substates with different SZ values are of the order of 1-10 cm-1, QTM occurs when energy levels of two substates coincide under an appropriate magnetic field and the two states are brought to resonance. In the [Pc2Tb] case, such level coincidence cannot occur with magnetic fields below several tesla, because the lowest substates are separated from the rest of the substates by a few hundred per centimeter. The steps observed for [Pc2Tb] must therefore be caused by a different mechanism. 

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