First-principles studies of the geometry and energetics of the ${\mathrm{Si}}_{36}$ cluster

First-principles studies of the geometry and energetics of the ${\mathrm{Si}}_{36}$ cluster are performed by searching 17 structural isomers including cage, wire, and stuffed fullerene. It is found that the tricapped-trigonal-prism unit is not the structural unit for ${\mathrm{Si}}_{36},$ and the stable structure is identified to have a more spherical geometry derived from the stuffed fullerene configurations. This is in agreement with the experiment which suggested a structural transition from the elongated geometry to a more spherical one for the medium sized silicon cluster [Hudgins et al., J. Chem. Phys. 111, 7865 (1999); Bergeron et al., J. Chem. Phys. 117, 3219 (2002)].