Clusters alkali

Small metal clusters have received considerable attention because of their possible involvement as "active sites" in a variety of catalyzed reactions. Although not particularly noted for their catalytic activity, alkali clusters have a simple chemical composition and may, therefore, model the more complicated systems in a manner analogous to the role played by the hydrogen atom in atomic structure. Less emphasized is the fundamental nature of alkali clusters per se. Since the ground state of Hj is not chemically bound, alkali trimers are the most elementary species which can exhibit a Jahn-Teller interaction. 

If the octahedral and icosahedral 13-atom nickel clusters are representative, an inhomogeneous magnetic field is not a good tool for separating isomers of transition metal clusters. This result is reminiscent of the fact that geometry plays no strong role in the ionization potential variation of alkali clusters (80). However, many calculations must be made before we can be definitive here. 

Charge transfer (ct) represents one of the most frequently studied phenomena in the field of ion-atom scattering [6] and has been intensively for ion-surface interactions [7] as well. In order to close this gap, there has been a great experimental effort on ct in cluster collisions [8-13]. Here in Sect. 4, we present two systematic investigations of recent experiments of ct measuring 1) integral ct cross sections for various alkali clusters [14,15], and 2) the laser-enhanced charge transfer for small sodium clusters [16]. 

A cluster is an assembly of identical objects whose total number can be chosen at will. An atomic cluster is therefore an assembly of atoms in which the total number is adjustable. Just as, in solid state physics, one distinguishes between cases in which the valence electrons become mobile and those in which they remain localised on individual atomic sites, so one finds different kinds of clusters, depending on the degree of localisation of the valence electrons. Broadly speaking, these differences are dictated by the periodic table at one extreme, one has the rare-gas clusters, in which electrons remain localised, while at the other, one finds the alkali clusters, which are metallic in the sense that the valence electrons can move throughout the cluster. 

Fig. 12.7. Radial potential and charge density for an alkali cluster of 20 atoms, as obtained from the jellium model. Note the FYiedel oscillations in the density of electronic charge. The ion density is assumed to be a top hat function (after W. Ekardt [685]).

We suppose that there is only one delocalised electron per site (an appropriate assumption for an alkali cluster). The Hiickel Hamiltonian for the cluster can then be written as ... 

Kresin V V, Tikhonov G, Kasperovich V, Wong K and Brockhaus P 1998 Long-range van der Waals forces between alkali clusters and atoms J. Chem. Phys. 108 6660... 

Experiments on noble metal clusters (Cun, AgN, Aun) indicate the existence of shell-effects, similar to those observed in alkali clusters. These are reflected in the mass spectrum [10] and in the variations of the ionization potential with N. The shell-closing numbers are the same as for alkali metals, that is N = 2,S,20,40, etc. Cu, Ag and Au atoms have an electronic configuration of the type nd °(n + l)s so the DFT jellium model explains the magic numbers if we assume that the s electrons (one per atom) move within the self-consistent, spherically symmetric, effective jellium potential. 

In general, the presence of the impurity atom induces a strong perturbation of the electronic cloud of an alkali cluster. The different nature of the impurity can be accounted for by a simple extension of the jellium model. The foreign atom is assumed to be at the cluster centre, and both subsystems - impurity and host - are characterized by different ionic densities in a jellium-like description. The following positive-charge background is then assumed ... 

Linear response theory (TDLDA) applied to the jellium model follows the Mie result, but only in a qualitative way the dipole absorption cross sections of spherical alkali clusters usually exhibit a dominant peak, which exausts some 75-90% of the dipole sum rule and is red-shifted by 10-20% with respect to the Mie formula (see Fig. 7). The centroid of the strength distribution tends towards the Mie resonance in the limit of a macroscopic metal sphere. Its red-shift in finite clusters is a quantum mechanical finite-size effect, which is closely related to the spill-out of the electrons beyond the jellium edge. Some 10-25% of the... 

The systematically performed pump-probe spectroscopy on alkali clusters provided a good indication about suited candidates for a coherent control experiment. Among these, the fragmentation dynamics of the heteronu-clear trimer Na2K appeared to us the best. The corresponding pump-probe spectrum is shown in Fig. 14(a). It clearly exhibits — superimposed on an exponential decay with a time constant of 3.28 ps — an oscillatory behaviour with a period of roughly 500 fs. The Fourier-transform of this... 

Plotted as a function of N, the calculated ionization potentials of alkali clusters display the expected drops at N = 8, 18, 20, 34, 40,... Nevertheless, the magnitude of the oscillations of I is overestimated in the jellium model. 

Clemenger [42] has studied the effect of ellipsoidal deformations in alkali clusters with N less than 100, using a modified three-dimensional harmonic oscillator model. The model considers different oscillator frequencies along the z axis (taken as symmetry axis) and perpendicular to the z axis. The model Hamiltonian used by Clemenger also contains an anharmonic term. Its purpose is to flatten the bottom of the potential well and to make it to resemble a rounded square-well potential. 

The deformation parameter rj describes how prolate or oblate the cluster is. This parameter was determined by minimizing the total energy calculated by adding the eigenvalues of the occupied electronic states. For alkali clusters with N less than 100, values up to q = 0.5 are estimated for open-shell clusters. The main first order effects of the ellipsoidal model are energy shifts that are proportional to q. The ellipsoidal model explains well the fine-structure features of the mass spectra [25], that is, those features which are beyond the realm of the spherical jellium model. 

From the odd-even effects observed in the ionization potential and electron affinity of small clusters (see Sect. 2.4) we can also expect odd-even oscillations in the reactivity. For instance, the ionization potential I(Np) of a small alkali cluster with an even number of atoms (Np) is larger than I(Np -i- 1) and I(Np — 1). At the same time the electron affinity A(Np) is smaller than A(Np -I- 1) and A(Np — 1). Consequently I(Np) —A(Np) will be larger than I(Np-I- 1) — A(Np -I- 1) or I(Np — 1) — A(Np — 1). In summary, the spin pairing effect induces odd-even oscillations in the reactivity. 

C. Brechnignac, P. Cahuzac, J.P. Roux, D. Davolini, F. Spiegehnann, Adiabatic decomposition of mass-selected alkali clusters. J. Chem. Phys. 87,3694 (1987)... 

Rayane D, AUouche AR, Benichou E et al (1999) Static electric dipole polarizabilities of alkali clusters. Eur Phys 19 243-248... 

Early interest in heteroatom clusters having alkali metals as the host was academic rather than dictated by precise observations. The main question regarded the extent to which the jellium-derived shell model retained its validity. However, this question was approached on the basis of oversimplified structural models in which the heteroatom (typically a closed-shell alkali-earth such as Mg) was located at the center of the cluster [235, 236]. In this hypothetical scheme, the perturbation of the electronic structure relative to that of the isoelectronic alkali cluster is somewhat trivial for instance, in the Na Mg system the presence of Mg would only alter the sequence of levels of the shell jellium model from Is, Ip, Is, 2s,. .. (appropriate to sodium clusters) to Is, Ip, 2s, Id,. .. (see also [236]). This would lead to the prediction that Na6Mg and NasMg are MNs. 

In Figure 5.8 the dependence of the average line width for Na4 " and Nas" " is plotted as a function of cluster temperature. The line width increases with the square root of the temperature. For the smallest cluster, Na4 ", one very small individual resonance was measured. A comparison of this resonance at 35 K and 100 K is given in Figure 5.9. The line width increases by a factor of two upon the threefold increase of temperature, whereas the oscillator strength in this resonance remains unchanged at (5ib ) 10 per 3s electron. This is the narrowest resonance ever found in alkali clusters, and could therefore serve as a stringent test for theory. 

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