Electronic shell effects

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]. 

Electronic shell effects are evident in the case discussed here, and affect many others. The separation of F into the two terms of Eq. (49) is useful, because the shell effects are concentrated in AHf, as early studies had already hinted [75,84]. For this reason calculation of B has also been performed, using a simple version of DFT, namely an extended Thomas-Fermi (ETF) approximation, within the framework of the TJSM [81,82]. The ETF functional differs from that in Eq. (11) in the kinetic energy, which is approximated by ... 

It was mentioned in Sect. 4 that electronic-shell effects appear in the mass abundance [10,43], ionization potentials [88], and electron affinities [89] of noble metal clusters that are very similar to those observed for alkalis. These can be readily interpreted within the spherical jellium model if we treat the noble metal atoms as monovalent, that is, each atom contributes its external s-el tron only. Even more, odd-even effects are also observed for small N in the properties mentioned above, and have been explained by Penzar and Ekardt [32] within the context of the spheroidally deformed jellium model. 

How can the transition from shells of electrons to shells of atoms be interpreted Small sodium clusters are soft. There is no difficulty for the atoms to arrange themselves into a spherical conformation if this is demanded by the closing of an electronic shell or for the cluster to adopt deformed shapes in the case of oi n electronic shells. That is, smaU clusters behave like soft droplets, not necessarily liquid. When the size reaches about 1500 atoms, the electronic shell effects have become less intense and, consequently, changes in the global cluster shape become more difficult to attain. Under these circumstances, the formation... 

The asymptotic expressions of I and A arc valid in the limit of large cluster size. Also for small or intermediate size those expressions are useful. They give the average variation of I and A with R, but two distinct types of deviations have been found from the average curve electronic shell effects and odd-even effects. 

Electronic shell effects are well known in clusters of the monovalent metals alkali and noble metals. The experimental ionization potential of alkali metal clusters [25] decays with R following Eq. (1), but superimposed to this average behavior there are pronounced drops between cluster size N and N -i- 1 for some particular values of N, namely N = 8, 18, 20, 40, 58, 92,... 

At low energies electron shell effects should also be taken into account by using the C/Z shell correction, see (Groom etal. 2001) for details. The Bethe-Bloch equation (O Eq. (8.1)) is based on first-order Born approximation. Higher order effects, important at low energies only, can be included by adding a term z L2(P ) in the square brackets of Eq. (8.1) where L2(P ) is an empirical function of particle speed. 

Electronic Shell Effects in Monomer and Dimer Separation Energies... 

Electronic Shell Effects in Fission Barriers and Fission Dynamics of Metal Clusters... 

It can be seen that the LDM barrier is either absent or very small, and that the total barrier is due almost exclusively to electronic shell effects. The total barrier has a doublehumped structure, with the outer hump corresponding to the LDM saddle point, which also happens to be the scission point (indicated by an empty vertical arrow). The inner hump coincides with the peak of the shell-effect term, and is associated with the rearrangement... 

Experimental evidence for electronic shells is foimd in the plot of cluster abundance vs. nuclearity and in the variation of the ionization energies of clusters (see Fig. 1.12). Electronic shell effects dominate the properties of alkali metal clusters. They are also broadly apphcable to p-block metals. The properties of transition and nobel metal nanoparticles, however, are influenced more by the formation of geometric shells. In fact, a transition from shells of electrons to shells of atoms is seen in the case of A1 [29,53]. It appears that the abundance of available oxidation states and the directional nature of the d- and f-orbitals (and to a limited extent, of the p-orbital) play a role in determining the shell that governs the property of a particular cluster. 

The approaches we have discussed in the preceding section were based on the rationale that for metal clusters, there is no directional bonding and, instead, the electrons are delocalized over the complete system. Thereby, particularly stable clusters (i.e., magic numbers) occur for clusters for which the atoms can form a particularly compact, close-packed geometrical structure. The electronic effects were at most indirectly induded so that, e.g., stability due to electronic shell effects is not taken into account. 

As we have learnt, alkali and noble metal clusters are the ideal realizations of shell models. What happens when a TM atom is added to an alkali or a noble metal cluster is an interesting issue since TM atoms have both delocalized s and localized d electrons. In fact, these bimetallic clusters show a fascinating combination of electronic shell effects, and magnetic properties, as we will discover. 

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