Application of a parallel genetic algorithm to the global optimization of medium-sized Au–Pd sub-nanometre clusters

Abstract

Abstract. To contribute to the discussion of the high activity and reactivity of Au-Pd system, we have adopted the BPGA-DFT approach to study the structural and energetic properties of medium-sized AuPd sub-nanometre clusters with 11-18 atoms. We have examined the structural behaviour and stability as a function of cluster size and composition. The study suggests 2D-3D crossover points for pure Au clusters at 14 and 16 atoms, whereas pure Pd clusters are all found to be 3D. For Au-Pd nanoalloys, the role of cluster size and the influence of doping were found to be extensive and non-monotonic in altering cluster structures. Various stability criteria (e.g. binding energies, second differences in energy, and mixing energies) are used to evaluate the energetics, structures, and tendency of segregation in sub-nanometre Au-Pd clusters. HOMO-LUMO gaps were calculated to give additional information on cluster stability and a systematic homotop search was used to evaluate the energies of the generated global minima of monosubstituted clusters and the preferred doping sites, as well as confirming the validity of the BPGA-DFT approach.

Effect of palladium doping on the stability and fragmentation patterns of cationic gold clusters

“…5d electrons are partially involved in the bonding between the atoms and thus gold clusters adopt structures very different from clusters of other elements [8]. For example, ion mobility experiments have shown that negatively charged gold clusters are planar up to N = 11 [9], whereas recent calculations predicted that neutral species can be planar up to the surprisingly large number of 13 atoms [10]. For positively charged clusters, the 2D to 3D transition is known to take place at N = 9, with Au 8…”

“…Doping can significantly influence the stability of a cluster; first, by altering the system's atomic structure, thus modifying the shape of the "box" confining the delocalized electrons, and second, by changing the number of valence electrons available for delocalization, which may lead to new shell closings [12,19,20]. From a fundamental point of view, Pd doping is a very interesting case for study because of its ground-state electronic configuration, with a closed 4d shell and no valence s electrons ([Kr]4d 10 ). Photoelectron spectroscopy measurements on small Pd-doped anionic gold clusters, PdAu N − (N = 1-4), suggested that the Pd-dopant atom is excited to a [Kr]4d 9 5s 1 state, after which the Pd valence s electron is delocalized and participates in the metallic bonding [21].…”

First principles global optimization of metal clusters and nanoalloys

“…Johnston et al used the BPGA-DFT approach to perform a systematic search for the GM of neutral Au n Pd m clusters (n + m = 4-10) [204], finding that Pd-rich clusters tend to adopt 3D geometries, whereas 2D geometries are only obtained for gold clusters doped with at most one Pd atom. In a subsequent investigation, medium-sized Au-Pd clusters with 11-18 atoms were globally optimized employing the BPGA with spin polarized DFT [205].…”

A Cyclical Non-Linear Inertia-Weighted Teaching–Learning-Based Optimization Algorithm

“…In the past decades, many classical nature-inspired optimization algorithms based on population have been proposed. These algorithms have been proven effective in solving global optimization problems and specific types of engineering optimization problems, such as GA (genetic algorithm) [1,2], ACO (ant colony optimization) [3,4], PSO (particle swarm optimization) [5,6], ABC (artificial bee colony) [7][8][9] and DE (differential evolution) [10][11][12], etc. However, any algorithm has its own merits and demerits in solving diverse problems.…”