Geometric and electronic properties of AulPtm (l + m ≤ 10) clusters: a first-principles study

Abstract

The structural evolutions and electronic properties of Au_lPt_m (l + m ≤ 10) clusters are investigated by using the first-principles methods. We use the inverse design of materials using the multi-objective differential evolution (IM²ODE) package to globally search the equilibrium structures and investigate the evolving trend from a two-dimensional structure to a three-dimensional structure on horizontal extension and vertical extension for Au_lPt_m (l + m ≤ 10) clusters. The three-dimensional stable geometry of Au₈Pt and Au₈Pt₂ is discovered for the first time in our work. We also notice that the equilibrium structures of Au_lPt_m (l + m = 10 and l ≤ 8) tend to form a tetrahedral geometry and can be obtained by replacing the Au atom in the most stable structure of Au_l+1Pt_m−1 with the Pt atom, where Pt atoms assemble together and occupy the center of clusters and Au atoms prefer to lie on the vertex or edge position. The average binding energy (E_b) is mostly decided by Pt–Pt bond numbers, namely the numbers of Pt atoms, followed by Au–Pt bond numbers. The second-order energy difference (Δ₂E_v and Δ₂E_h) and the nearest-neighbor energy difference (Δ₄E_nn) show that Au₆Pt, Au₄Pt₂, Au₃Pt₃, Au₂Pt₄ and AuPt₇ clusters exhibit high relative physical stability, so we suggest that these clusters could be defined as the magic number clusters for Au_lPt_m (l + m ≤ 10) clusters. The HOMO–LUMO energy gap (E_g), adiabatic ionization potential (AIP) and the adiabatic electron affinity (AEA) are also investigated to elaborate the relative electronic stability of all the clusters.