Revisit of Sin (n=21-29) Clusters by Ab Initio Global Search

Using our improved genetic algorithm combined with density functional theory calculations, we perform unbiased global search for the most stable structures of Si-n clusters with n = 21-29. A new principal direction crossover operation is introduced to search the prolate structures on the potential energy surface. We confirmed previous results for most sized Si-n clusters and find more stable structure at n = 23 and 26. In particular, we find a new endohedral cage structure at Si-23, which is 0.4 eV lower in energy than previously reported prolate structure and exhibit a distinct peak on the second order difference of total cluster energy. We discuss the competition between prolate and spherical motifs in the medium-sized Si-n clusters in light of binding energy and HOMO-LUMO gap. The transition of structural motif from prolate to near spherical in Si-n clusters occurs at n = 26. The outer cages are composed of pentagon, hexagon, quadrangle and heptagon, with one to three interior atoms filled inside the cage. These results establish a more complete picture for the structural evolution of the medium-sized silicon clusters. Average bond lengths and Mayer bond order are also discussed.