Abstract
We study the melting of small sodium clusters ${\mathrm{Na}}_{N}$ $(N=8,20,40)$ and ${\mathrm{Na}}_{N}^{+}$ $(N=53\ensuremath{-}57,93,139,147)$ using an ab initio treatment of valence electrons within the extended Thomas-Fermi approximation. The ionic entropy and specific heats are extracted using a multiple-histogram analysis. The smaller clusters show multi-process melting, while the larger clusters favor predominantly single-process melting. We find a pronounced maximum in the melting point around $N=55.$
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