Small Sodium Clusters

Sodium clusters seem to be the most extensively studied species in cluster science. From a theoretical point of view they can be regarded as a prototype 

These equations nicely demonstrate that Type II processes will be detected in the detection channel of NaJ, NaJ, and Nay. This result is as well 

The real-time spectra indeed reveal this predicted behavior (see Fig. 4.11). The spectra were analyzed within the extended fragmentation model (see Sect. 2.2.2). For clusters with an odd number of atoms a fairly large number of Type II clusters is observable(Fig. 4.12 a), which is in excellent agreement with the reaction equations given above. The real-time spectra of clusters with an even number of sodium atoms show a decay which can be described 

Besides the distinct even-odd alternation for both excitation energies, an obvious change with n = 5 appears. For E pump = 1.48 eV the even-odd alternation is drastically enhanced. Here, compared to Nas, the fragmentation probability of Naio is about 8 times bigger. For E pump — 2.96 eV the frag- 

It has to be stated that this simple fragmentation model cannot explain any energy dependence of the recorded data. For other excitation conditions, e.g. as used by Gerber and coworkers in their experiments on Na, the model might lose its validity. For example, Gerber and coworkers [71, 132] excited Nas close to four surface plasmon resonances at 2.39eV (518nm). Therefore, several ultrashort decay processes are involved simultaneously, instead of one in the case discussed here. 

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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]. 

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... 

While the dipole absorption features [114, 124] and photodissociation dynamics of small sodium clusters are rather well known [112, 113, 126, 127, 407-409], there is very little knowledge about potassium clusters larger than the dimer. The lack of experimental data might be caused by ultrafast fragmentation processes within the potassium clusters, so that conventional stationary spectroscopic techniques might fail. Hence, the goal of this section is to determine the photodissociation probability of small potassium clusters as a function of cluster size as well as excitation energy. 

In order to study the dynamics of small sodium clusters at finite temperatares Born-Oppenheimer molecular dynamics (BOMD) calculations were performed at the above described PBE/DZVP/A2 level of theory. For each cluster, from the dimer to the nonamer, 18 trajectories were recorded in a temperature range from 50 to 900 K with intervals of 50 K. Each trajectory has a length of 220 ps and was recorded with a time step of 2 ps. Similar statistics have already been successfully applied to determine the melting temperatures of sodium clusters with LDA pseudo-potential DFT molecular dynamics (Chacko et al. 2005). 

Recent experiments by Citrin and coworkers (41) have clarified the role of the support in photoemission from small metal clusters. They condensed several monolayers of krypton onto either platinum or sodium metal substrates. By varying the thickness of the krypton from one to ten monolayers, the surface could be converted from metal to semimetal to insulator. The krypton peak position provides a direct measure of the sample vacuum level (32). The krypton layers are thin, less than 10 monolayers, so that the vacuum level is determined by the metal substrate. Onto the krypton layers, sodium clusters were deposited at varying coverages. Shifts in the Kr 4s and Na 2p binding energies were recorded relative to the Fermi level of the grounded substrate. 

Supersonic expansions have been used to form small metal aggregates, (2 < n < 4). Emphasis is placed on the analysis of bound-free transitions in these small metal clusters. Discussion focuses on the characterization of variously produced sodium supersonic expansions and the analysis of laser Induced atomic fluorescence resulting from the photodissociation of triatomic sodium clusters. We will consider (1) the nature of observed "fluctuation" bands corresponding to bound-free transitions involving a repulsive excited state which dissociates to yield (Na-D line) sodium atoms and ground state,, ... 

The transition from the atom to the cluster to the bulk metal can best be understood in the alkali metals. For example, the ionization potential (IP) (and also the electron affinity (EA)) of sodium clusters Na must approach the metallic sodium work function in the limit N - . We previously displayed this (1) by showing these values from the beautiful experiments by Schumacher et al. (36, 37) (also described in this volume 38)) plotted versus N". The electron affinity values also shown are from (39), (40) and (34) for N = 1,2 and 3, respectively. A better plot still is versus the radius R of the N-mer, equivalent to a plot versus as shown in Figure 1. The slopes of the lines labelled "metal sphere" are slightly uncertain those shown are 4/3 times the slope of Wood ( j ) and assume a simple cubic lattice relation of R and N. It is clear that reasonably accurate interpolation between the bulk work function and the IP and EA values for small clusters is now possible. There are, of course, important quantum and statistical effects for small N, e.g. the trimer has an anomalously low IP and high EA, which can be readily understood in terms of molecular orbital theory (, ). The positive trimer ions may in fact be "ionization sinks" in alkali vapor discharges a possible explanation for the "violet bands" seen in sodium vapor (20) is the radiative recombination of Na. Csj may be the hypothetical negative ion corresponding to EA == 1.2 eV... 

However, the most striking features of Figure 5.10 are the pronounced peaks at AT = 2, 8, 18, 20, 34,40 and 58. At the magic numbers the hardness shows a local maximum. Increased stability is accompanied by increased hardness. Identical results have been calculated for sodium clusters.Similar, but not so spectacular, resuls may be calculated for small silicon clusters. 

Hakkinen H, Barnett R N and Landman U 1995 Energetics, structure, and excess electrons in small sodium-chloride clusters Chem. Phys. Lett 232 79... 

From the optical response feature of the left-hand side of Figure 2.10 it is possible to conclude that classification according to the different characteristics expected for the F-center cuboid as compared with noncuboid clusters [41] has not been found in the optical response of small sodium fluoride clusters. This illustrates clearly that stmctural properties alone are not sufficient for classification of the cluster characteristics. 

In summary, we have shown that small sodium fluoride and lithium hydride clusters with one and two excess electrons exhibit their own characteristic absorption patterns. 

The first depletion spectra obtained for neutral sodium clusters N = 2-40 were characterized by structureless broad features containing one or two bands. The results were interpreted in terms of collective resonances of valence electrons (plasmons) for all clusters larger than tetramers [2, 52-55]. The analogies between findings for metallic clusters and observations of giant dipole resonances in nuclei have attracted a large attention. Therefore the methods employed in nuclear physics, such as different versions of RPA in connection with the jellium model, have also been applied for studying the optical properties of small clusters. Another aspect was the onset of conductivity in metal-insulator transitions. 

There exists only one measurement of the lifetime for a free sodium cluster ion that gives for the lifetime of the collective resonance of Na93 " a value of = 10 to 20 fs [56]. This would correspond to a lifetime broadening of only f = 33 to 66 meV. From this one can conclude that (1) the plasmon lifetime contribution to the width of one single peak is small, and (2) the near-Lorentzian shape of a single line is not due to the lifetime. 

The existence of discrete electronic states of electrons confined in a small metal cluster has been observed to influence the thermodynamic stability of the system, in particular during the production of sodium clusters in supersonic beams composed of the metal vapor and an inert gas. The statistics of the relative abundances of different particle sizes reveal the existence of magic numbers for the number of atoms in the cluster, A = 8, 20,40,58, 92,... [3.9]. This has been interpreted in terms of the existence of degenerate energy levels in a spherical well with infinite-potential walls. Particularly stable structures are obtained when the number of valence electrons is such that it leads to a closed-shell electronic structure, i. e. a structure with a completely filled energy level and an empty up-... 

The vitron theory is probably related to the later iceberg theory, namely, the tendency of silica to form small immiscible clusters in melts of lower alkali content (205). In sodium silicate glass with a SiOicNajO ratio of 7 1, the model predicts collidal silica units or particles about 1.9 nm in diameter. 

In this book the real-time photodissociation dynamics of small sodium (Nan=3...io) and potassium (Kn=3...9) clusters are studied as a function of cluster size as well as excitation wavelength (Sects. 4.2-4.4). The ratio of dissociative to radiative decay is a measure of the predissociation of an electronic state [122, 133]. For the C state of Naa the electronic predissociation dynamics and especially the localization of its onset are analyzed in detail by ultrafast spectroscopy (Sect. 4.1). 

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