Shapes and free energies of molten sodium clusters

The shell-correction method is formulated to calculate the shapes and free energies of hot alkali clusters. The equilibrium shapes of Na clusters with mass 50-700 are calculated by minimizing simultaneously with respect to two deformation parameters. For T = 700 degrees K strong deviations from spheroidal shape including reflection asymmetric shapes are found to survive in the center of the open shells. The second derivative of calculated free energy correlates with the derivative of the experimental cluster abundances, showing prominent spikes related to the change between spherical and deformed shape.