Structural, Relative Stable, and Electronic Properties of Pb n Sn n (n = 2–12) Clusters were Investigated Using Density Functional Theory

The structural, relative stable and electronic properties of Pb n Sn n (n = 2–12) alloy clusters were systematically studied using density functional theory. The isomers of Pb n Sn n alloy clusters were generated and determined by ab initio molecular dynamics. By comparing the calculated parameters of Pb 2 dimer and Sn 2 dimers with the parameters from experiments, our calculations are reasonable. With the lowest-energy structures for Pb n Sn n clusters, the average binding energies, fragmentation energies, second- order energy differences, vertical ionization potentials, vertical electron affinities, HOMO–LUMO gaps, and density of states were calculated and analyzed. The results indicate that the Sn atoms have a tendency to bond together, the average binding energies tend to be stable up to n = 8, Pb 8 Sn 8 cluster is a good candidate to calculate the molecular interaction energy parameter in Wilson equation, the clusters become less chemical stable and show an insulator-to-metallic transition, 3, 6, 8 and 11 are magic numbers of Pb n Sn n (n = 2–12) clusters, the charges always transfer from Sn atoms to Pb atoms in Pb n Sn n clusters except for Pb 10 Sn 10 cluster, and density of states of Pb n Sn n clusters becoming continuous and shifting toward negative with the increasing size n.