Structures and relative stability of medium-sized silicon clusters. IV. Motif based low-lying clusters Si\u3csub\u3e21\u3c/sub\u3e–Si\u3csub\u3e30\u3c/sub\u3e

Structures and relative stability of four families of low-lying silicon clusters in the size range of Sin(n=21–30) are studied, wherein two families of the clusters show prolate structures while the third one shows near-spherical structures. The prolate clusters in the first family can be assembled by connecting two small-sized magic clusters Sin(n=6, 7, 9, or 10) via a fused-puckered-hexagonal-ring Si9 unit (a fragment of bulk diamond silicon), while those in the second family can be constructed on the basis of a structural motif consisting of a puckered-hexagonal-ring Si6 unit (also a fragment of bulk diamond silicon) and a small-sized magic cluster Sin(n=6, 7, 9, or 10). For Si21–Si29, the predicted lowest-energy clusters (except Si27) exhibit prolate structures. For clusters larger than Si25, the third family of near-spherical clusters becomes energetically competitive. These near-spherical clusters all exhibit endohedral caged-like structures, and the cages are mostly homologue to the carbon-fullerene cages which consist of pentagons and hexagons exclusively. In addition, for Si26–Si30, we construct a new (fourth) family of low-lying clusters which have “Y-shaped” three-arm structures, where each arm is a small-sized magic cluster (Si6, Si7, or Si10). Density-functional calculation with the B3LYP functional shows that this new family of clusters is also energetically competitive, compared to the two prolate and one near-spherical low-lying families