Sodium clusters binding energy

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. 

The results obtained by Citrin and coworkers are shown in Figure 3. For sodium clusters on a metal support (wigl ML Kr/Pt, filled circles), the Kr 4s binding energy decreases with cluster coverage. This shows that the Fermi levels of the sodium and platinum equilibrate. As the sodium is added, the work function decreases from the value for platinum to the value for a sodium film. Conversely, the Na 2p peak position does not shift with cluster coverage. The rapid electron transfer between the sodium and platinum prevents any accumulation of charge on the cluster in the photoemission final state (41). 

FIG. 20. The periodically varying contribution to the calculated binding energy of spherical sodium cluster. The periodic variations are due to the quantized motion of the electrons in the background potential [71,153]. 

Sodium vapour, or other alkaline vapours, can be expanded supersonically from a hot stainless steel oven with a fine exit nozzle, resulting in well focussed cluster beams. Clusters form as a result of collisions between Na atoms in the tiny expansion zone, terminating some tenths of a millimeter beyond the nozzle. The clusters warm up because the condensation is an exothermic reaction, so there also is a tendency for evaporation from the clusters. As the expansion proceeds, collisions between Na atoms end and the tendency of atoms to evaporate from the hot clusters dominates. Each cluster loses mass and cools down. In the evaporation chains, clusters with low evaporation rates, i.e., with strong binding energies, tend to become abundant. 

A FIGURE 11.9 Average binding energy per atom for small clusters of lithium and sodium. 

Chandrakumar, K. R. S., Ghanty, T. K., Ghosh, S. K. (2004). Static dipole polarizability and binding energy of sodium clusters Na ( = 1 - 10) A critical assessment of all-electron based post-Hartree-Fock and density functional methods. Journal of Chemical Physics, 120, 6487. 

The conventional approach to calculate the polarizability of metal clusters is to solve the Kohn-Sham equations using suitable approximate forms for the exchange correlation functionals and a finite field method. We have recently carried out a systematic all electron DFT-based calculations for the polarizability and binding energy of sodium as well as lithium metal clusters [51,52]. It has been shown that the effect of electron correlation plays a significant role in determining the polarizability of metal clusters, although the effect is less pronounced for lithium clusters. Electron... 

As shown in previous publications relative to absorption spectroscopy and ground-state equilibrium geometries, the sodium atom in a 3s state prefers to bind on the surface of a rare-gas cluster. This stems from the fact that the NaAr diatomics have a smaller bonding energy at a longer intemuclear distance than ArAr, in concordance with the rather large size of the isotropic 3 s orbital. 

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