Sodium clusters total energies

Fig. 5.3 The total energy per atom of sodium clusters versus the number of atoms in the cluster, evaluated within the self-consistent jellium model. (From Cohen (1987).)...

Finite differences, finally, is the simplest approach the total energy and dipole moment are computed as a function of the strength of the external electric field. Then, a quadratic fit to the energy or, equivalently, a linear fit to the dipole moment as a function of the external field amplitude provide the polarizability a. This direct approach has been used for sodium clusters in Refs [110] (LSD A) and [111] (LSD A and GGA), and for aluminum in Ref. [106] (LSDA). 

The details of the crossed-beam apparatus used in our experiment can be found in many earlier publications [17,18]. Briefly, the alkali dimer source consisted of a resistively heated molybdenum oven and nozzle assembly, with the temperatures of the nozzle and the oven being controlled independently by different heating elements. Sodium vapour carried by an inert gas, which was either He or Ne, expanded out of the 0.2 mm diameter nozzle to form a supersonic beam of Na/Na2/inert gas mixture. The Na2 concentration was about 5% molar fraction of the total sodium in the beam when He was used as carrier gas. The beam quality dropped severely when we seeded Na2 in Ne so the dimer intensity became much weaker. No substantial amount of trimers or larger clusters was detected under our experimental conditions. The Na2 beam was crossed at 90 by a neat oxygen supersonic beam in the main collision chamber under single collision conditions. The O2 source nozzle was heated to 473 K to prevent cluster formation. Both sources were doubly differentially pumped. The beams were skimmed and collimated to 2 FWHM in the collision chamber. Under these conditions, the collision energies for the reaction could be varied from 8 kcal/mol to 23 kcal/mol. 

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