Thermal properties of the valence electrons in alkali metal clusters

Abstract

Abstract. The finite-temperature density functional approach is applied for the first time to calculate thermal properties of the valence electron system in metal clusters using the spherical jellium model. Both the canonical and the grand canonical formalism are applied and their differences are discussed. We study the temperature dependence of the total free energy F(N) (including a contribution from the ionic jellium background) for spherical neutral clusters containing N atoms. We investigate, in particular, its first and second differences, A I F = F ( N -1 ) -F ( N )and A 2 F = F ( N + I ) + F ( N -1 ) -2F(N), and discuss their possible relevance for the understanding of the mass abundance spectra observed in cluster production experiments. We show that the typical enhancement of magic spherical-shell clusters with N = 8 , 20, 34, 40, 58, 92, 138, 186, 254, 338, 398, 440, 508, 6t2..., most of which are well established experimentally, is decreasing rather fast with increasing temperature T and cluster size N. We also present electronic entropies and specific heats of spherical neutral clusters. The Koopmans theorem and related approximations for calculating A~F and A2F at T > 0 are dis-

Modified Nilsson model for large sodium clusters

“…When comparing the fluctuations in the energies of Fig. 5a with those of spherical Kohn-Sham calculations [6,7,8], we note that the sharp minima at N= 676 and N = 832 are more pronounced in the present results than in the KS results ~. This has nothing to do with the effects of deformation, since these numbers correspond to spherical clusters, but is simply a consequence of the decreasing quality of our fit of the spherical KS spectrum shown in Fig.…”

“…5a, rather than with the second derivatives of the total free energy F as done recently with fully selfconsistent KohnSham results [6][7][8]. Our reason for not doing so here is that our present 0E as a function of particle number, due to the plateau uncertainties in the Strutinsky averaging, contains small high-frequency fluctuations to which the second (or even the first) derivatives are very sensitive [36].…”

“…We use (8) to determine (ho%) (N°) for each main shell N O using the weighted average (rZ)uo given by the KS results. 12 is no longer diagonal for ~ 4: 0.…”

“…Our reason for not doing so here is that our present 0E as a function of particle number, due to the plateau uncertainties in the Strutinsky averaging, contains small high-frequency fluctuations to which the second (or even the first) derivatives are very sensitive [36]. These fluctuations are expected to be strongly damped when a finite temperature of the electrons is included [8]. However, the extension of the Strutinsky method to finite temperatures, though formally possible (see, e.g., [25]), is numerically involved and would lead beyond the scope of our present simple model -the more so since also the temperature dependence of the LDM parameters is uncertain.…”

Selfconsistent calculation of electronic supershells in metal clusters

“…The experimental observation of supershell structure in cluster expansion sources is inhibited by the fact that the clusters so produced have, at least initially, a finite temperature which tends to reduce the shell effects [7,8,9]. Nevertheless, in the newest sodium vapour expansion experiments of the Copenhagen -Orsay -Stuttgart collaboration [1], a supershell beating in the mass abundance spectrum of sodium clusters has been put into evidence.…”