Melting of sodium clusters: where do the magic numbers come from?

Melting temperatures of Na clusters show size-dependent fluctuations that have resisted interpretation so far. Here we discuss that these temperatures, in fact, cannot be expected to exhibit an easily understandable behavior. The energy and entropy differences between the liquid and the solid clusters turn out to be much more relevant parameters. They exhibit pronounced maxima that correlate well with geometrical shell closings, demonstrating the importance of geometric structure for the melting process. Icosahedral symmetry dominates, a conclusion corroborated by new photoelectron spectra measured on cold cluster anions. In the vicinity of the geometrical shell closings the measured entropy change upon melting is in good agreement with a simple combinatorial model.