Stable Tin (n = 2-15) clusters and their geometries: DFT calculations

We present a detailed structural analysis for small Tin (n = 2-15) clusters based on ab initio quantum mechanical calculations of their binding energies, frontier orbital gaps, and second energy derivatives. Local density approximation calculations revealed that while the smaller clusters (n < or = 8) prefer hexagonal atomic arrays with bulklike crystal symmetry, the bigger clusters prefer pentagonal atomic arrays. From the stability criteria of the magic number clusters we could identify three magic number clusters Ti7, Ti13, and Ti15. While the most stable configuration of Ti7 is a decahedral bipyramid induced by tetrahedral atomic arrays, the most stable configuration of Ti13 is an icosahedron. The other stable cluster Ti15 takes a closed-shell icosahedron-like configuration with both pentagonal and hexagonal symmetries. The stability of the Tin clusters strongly depends on their geometries and charge states. The HOMO-LUMO gap of the Tin clusters approaches its bulk value for n > 8. While there is not much difference between the HOMO and LUMO isosurface charge distributions for the Ti7 and Ti13 clusters in their most stable configurations, they are very different in the case of Ti15. Such a distinct charge distribution in Ti15 indicates its singular chemical selectivity over the other two magic number clusters.