The chemical space of Pb_N−nBi_n and (Pb_N−nBi_n)⁺: A systematic study for N = 3–13

A systematic exploration of the energy hypersurfaces of three to 13-atomic neutral and cationic binary lead-bismuth clusters is presented. Global minima for all 99 compositions (N = 3–13, n = 0–N) were obtained by a density functional theory based genetic algorithm, which was applied to every single composition, both for the neutral clusters and for the cations. Within the genetic algorithm, the energetically most favorable assignment of atom types to atom positions was found via aimed swapping of element types, based on first-order perturbation theory in the nuclear charge. Results of the genetic algorithm procedure were refined with high-level density functional treatments including also the effects of spin-orbit coupling. The resulting global minima were analyzed applying various stability criteria, finally yielding the ∼20 overall most stable neutral and cationic clusters in the chemical space of three to 13-atomic mixed lead bismuth clusters. In most cases, they are polyhedrons that obey the Wade-Mingos rules.