The prolate-to-spherical shape transition in Group IV clusters has been a puzzle since its discovery over a decade ago. Here we explain this phenomenon by elucidating the structures of ${\mathrm{S}\mathrm{i}}_n$ and $\mathrm{S}\mathrm{i}_n{}^{+}$ with $n=20–27$. The geometries were obtained in unbiased searches using a new “big bang” optimization method. They are substantially more stable than any found to date, and their ion mobilities and dissociation energies are in excellent agreement with experiment. The present results prove that the packing of midsize clusters is thermodynamically controlled and open the door to understanding the evolution of semiconductor nanosystems towards the bulk.

• Received 11 December 2003

DOI:https://doi.org/10.1103/PhysRevLett.93.013401