Global geometry optimization of silicon clusters employing empirical potentials, density functionals, and ab initio calculations

Si-n clusters in the size range n = 4-30 have been investigated using a combination of global structure optimization methods with DFT and ab initio calculations. One of the central aims is to provide explanations for the structural transition from prolate to spherical outer shapes at about n = 25, as observed in ion mobility measurements. Firstly, several existing empirical potentials for silicon and a newly generated variant of one of them were better adapted to small silicon clusters, by global optimization of their parameters. The best resulting empirical potentials were then employed in global cluster structure optimizations. The most promising structures from this stage were relaxed further at the DFT level with the hybrid B3LYP functional. For the resulting structures, single point energies have been calculated at the LMP2 level with a reasonable medium-sized basis set, cc-pVTZ. These DFT and LMP2 calculations were also carried out for the best structures proposed in the literature, including the most recent ones, to obtain the currently best and most complete overall picture of the structural preferences of silicon clusters. In agreement with recent findings, results obtained at the DFT level do support the shape transition from prolate to spherical structures, beginning with Si-26 (albeit not completely without problems). In stark contrast, at the LMP2 level, the dominance of spherical structures after the transition region could not be confirmed. Instead, just as below the transition region, prolate isomers are obtained as the lowest-energy structures for n <= 29. We conclude that higher (probably multireference) levels of theoretical treatments are needed before the puzzle of the silicon cluster shape transition at n = 25 can safely be considered as explained.