Thermal properties of the valence electrons in alkali metal clusters

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 energyF(N) (including a contribution from the ionic jellium background) for spherical neutral clusters containingN atoms. We investigate, in particular, its first and second differences, Δ₁ F =F (N ? 1) ?F (N) and Δ₂ F =F(N + 1) +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 withN=8, 20, 34, 40, 58, 92, 138, 186, 254, 338, 398, 440, 508, 612..., most of which are well established experimentally, is decreasing rather fast with increasing temperatureT and cluster sizeN. We also present electronic entropies and specific heats of spherical neutral clusters. The Koopmans theorem and related approximations for calculating Δ₁ F and Δ₂ F atT > 0 are discussed.