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

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.