Global geometry optimization of silicon clusters described by three empirical potentials

The “basic-hopping” global optimization technique developed by Wales and Doye is employed to study the global minima of silicon clusters $Sin(3⩽n⩽30)$ with three empirical potentials: the Stillinger–Weber (SW), the modified Stillinger–Weber (MSW), and the Gong potentials. For the small-sized SW and Gong clusters $(3⩽n⩽15),$ it is found that the global minima obtained based on the basin-hopping method are identical to those reported by using the genetic algorithm [Iwamatsu, J. Chem. Phys. 112, 10976 (2000)], as well as with those by using molecular dynamics and the steepest-descent quench (SDQ) method [Feuston, Kalia, and Vashishta, Phys. Rev. B 37, 6297 (1988)]. However, for the mid-sized SW clusters $(16⩽n⩽20),$ the global minima obtained differ from those based on the SDQ method, e.g., the appearance of the endohedral atom with fivefold coordination starting at $n=17,$ as opposed to $n=19.$ For larger SW clusters $(20⩽n⩽30),$ it is found that the “bulklike” endohedral atom with tetrahedral coordination starts at $n=20.$ In particular, the overall structural features of SW $Si21,$ $Si23,$ $Si25,$ and $Si28$ are nearly identical to the MSW counterparts. With the SW $Si21$ as the starting structure, a geometric optimization at the B3LYP/6-31G(d) level of density-functional theory yields an isomer similar to the ground-state- isomer of $Si21$ reported by Pederson et al. [Phys. Rev. B 54, 2863 (1996)].