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We have performed unconstrained search for low-lying structures of medium-sized silicon clusters Si(31)-Si(40) and Si(45), by means of the minimum-hopping global optimization method coupled with a density-functional based tight-binding model of silicon. Subsequent geometric optimization by using density-functional theory with the PBE, BLYP, and B3LYP functionals was carried out to determine the relative stability of various candidate low-lying silicon clusters obtained from the unconstrained search. The low-lying characteristics of these clusters can be affirmed by comparing the binding energies per atom of these clusters with previously determined lowest-energy clusters(Si(n)) in the size range of 21</=n</=30. In view of the fact that there exist numerous low-lying "endohedral fullerenelike" isomers for each size in the range 30</=n</=40, we used the homologue carbon-fullerene cage to classify different families of isomers. This structural classification allows us to focus on generic features of various isomers and to group many apparently different isomers into a single family. In addition, we report a new family of low-lying clusters which have "Y-shaped three-arm" structures. Isomers in this "handmade" family can be energetically competitive as the endohedral fullerene isomers when the total energies are calculated with the BLYP or B3LYP functional.

Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31–Si40 and Si45