A genetic algorithm approach is applied to the optimization of the potential energy of a wide range of binary metallic nanoclusters, Ag-Cu, Ag-Ni, Au-Cu, Ag-Pd, Ag-Au, and Pd-Pt, modeled by a semiempirical potential. The aim of this work is to single out the driving forces that make different structural motifs the most favorable at different sizes and chemical compositions. Paper I is devoted to the analysis of size-mismatched systems, namely, Ag-Cu, Ag-Ni, and Au-Cu clusters. In Ag-Cu and Ag-Ni clusters, the large size mismatch and the tendency of Ag to segregate at the surface of Cu and Ni lead to the location of core-shell polyicosahedral minimum structures. Particularly stable polyicosahedral clusters are located at size N = 34 (at the composition with 27 Ag atoms) and N = 38 (at the composition with 32 and 30 Ag atoms). In Ag-Ni clusters, Ag32Ni13 is also shown to be a good energetic configuration. For Au-Cu clusters, these core-shell polyicosahedra are less common, because size mismatch is not reinforced by a strong tendency to segregation of Au at the surface of Cu, and Au atoms are not well accommodated upon the strained polyicosahedral surface.

Global optimization of bimetallic cluster structures. I. Size-mismatched Ag–Cu, Ag–Ni, and Au–Cu systems

The application of the ab initio genetic algorithm with an embedded gradient has been carried out for the elucidation of global minimum structures of a series of anionic sodium chloride clusters, Na(x)Cl(x+1) (-) (x=1-4), produced in the gas phase using electrospray ionization and studied by photoelectron spectroscopy. These are all superhalogen species with extremely high electron binding energies. The vertical electron detachment energies for Na(x)Cl(x+1) (-) were measured to be 5.6, 6.46, 6.3, and 7.0 eV, for x=1-4, respectively. Our ab initio gradient embedded genetic algorithm program detected the linear global minima for NaCl(2) (-) and Na(2)Cl(3) (-) and three-dimensional structures for the larger species. Na(3)Cl(4) (-) was found to have C(3v) symmetry, which can be viewed as a Na(4)Cl(4) cube missing a corner Na(+) cation, whereas Na(4)Cl(5) (-) was found to have C(4v) symmetry, close to a 3x3 planar structure. Excellent agreement between the theoretically calculated and the experimental spectra was observed, confirming the obtained structures and demonstrating the power of the developed genetic algorithm technique.

Structure of the Na x Cl x+1 - (x=1-4) clusters via ab initio genetic algorithm and photoelectron spectroscopy

We report the study of small lithium clusters Lin0/+1/-1 (n = 5−7), performed via the novel Gradient Embedded Genetic Algorithm (GEGA) technique and molecular orbital analysis. GEGA was developed for searching of the lowest-energy structures of clusters. Results of our search, obtained using this program, have been compared with the previous ab initio calculations, and the efficiency of the developed GEGA method has thus been confirmed. The molecular orbital analysis of the found Lin0/+1/-1 (n = 5−7) clusters showed the presence of multiple (σ and π) aromatic character in their chemical bonding, which governs their preferable shapes and special stability.

Search for the Lin(0/+1/-1) (n = 5-7) Lowest-Energy Structures Using the ab Initio Gradient Embedded Genetic Algorithm (GEGA). Elucidation of the Chemical Bonding in the Lithium Clusters.

Over the past decade, there has been a significant growth in the development and application of methods for performing global optimization (GO) of cluster and nanoparticle structures using first-principles electronic structure methods coupled to sophisticated search algorithms. This has in part been driven by the desire to avoid the use of empirical potentials (EPs), especially in cases where no reliable potentials exist to guide the search toward reasonable regions of configuration space. This has been facilitated by improvements in the reliability of the search algorithms, increased efficiency of the electronic structure methods, and the development of faster, multiprocessor high-performance computing architectures. In this review, we give a brief overview of GO algorithms, though concentrating mainly on genetic algorithm and basin hopping techniques, first in combination with EPs. The major part of the review then deals with details of the implementation and application of these search methods to allow exploration for global minimum cluster structures directly using electronic structure methods and, in particular, density functional theory. Example applications are presented, ranging from isolated monometallic and bimetallic clusters to molecular clusters and ligated and surface supported metal clusters. Finally, some possible future developments are highlighted. © 2013 Wiley Periodicals, Inc.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.24462

Global optimization of clusters using electronic structure methods

Novel implementation of the evolutionary approach known as particle swarm optimization (PSO) capable of finding the global minimum of the potential energy surface of atomic assemblies is reported. This is the first time the PSO technique has been used to perform global optimization of minimum structure search for chemical systems. Significant improvements have been introduced to the original PSO algorithm to increase its efficiency and reliability and adapt it to chemical systems. The developed software has successfully found the lowest-energy structures of the LJ26 Lennard-Jones cluster, anionic silicon hydride Si2H, and triply hydrated hydroxide ion OH− (H2O)3. It requires relatively small population sizes and demonstrates fast convergence. Efficiency of PSO has been compared with simulated annealing, and the gradient embedded genetic algorithm. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007

Global minimum structure searches via particle swarm optimization.

We present detailed numerical results on the ground state structures of metallic clusters. The Gupta-type many-body potential is used to account for the interactions between atoms in the cluster. Both the genetic algorithm technique and the basin hopping method have been applied to search for the global energy minima of clusters. The excellent agreement found in both schemes for the global energy minima gives credence to the optimized energy values obtained. For four monovalent and one polyvalent metals studied in this work and within the accuracy of the energies presented here, we find that the global energy minima predicted by the basin hopping method are the same as those values obtained by the genetic algorithm. Our calculations for the ground state energies of alkali metallic clusters show regularities in the energy differences, and the cluster growth pattern manifested by this same group of clusters is generally icosahedral, which is quite different from the close-packed and decahedral preferentially exhibited by the tetravalent lead clusters. Considering the inherent disparities in the electronic properties and the bulk structures in these metals (body-centered cubic for alkali metals and face-centered cubic for the lead metal), it is not unreasonable to conjecture that the valence electrons do play a subtle role in the conformation of metallic clusters.

Structures of metallic clusters: Mono- and polyvalent metals

A description of the concentration dependence of the magnetic susceptibilities of a number of liquid binary alloys of simple metals is effected in three stages. First, a previous pseudopotential formalism is extended to enable the calculation of the conduction electron diamagnetic susceptibilities in the pure liquid metals, Li, Na, K, Rb, Cs, In and Pb. These results are then combined with much earlier calculated values of the diamagnetic susceptibilities of the core electrons and with observed values, existing in the literature, of the total magnetic susceptibilities to infer the conduction electron paramagnetic susceptibilities of the above pure liquid metals. Second, the expressions for the two diamagnetic contributions are modified permitting the determination of their concentration dependence in a number of nearly-free-electron (NFE) like liquid binary alloys. The Landau theory of a Fermi liquid is used to infer the concentration dependence of the paramagnetic contribution. Third, Li-Pb, which is not NFE like over the entire concentration range is treated separately as a special but closely related case. The observed results for the concentration dependence of the total magnetic susceptibility are favourably reproduced, both for those alloy systems exhibiting smooth variations and for those with large variations.

Magnetic susceptibilities of liquid binary alloys

The composition dependence of the order-disorder critical temperature is investigated using the coherent potential approximation in the virtual crystal limit This simple band model allows the authors to explain the shift of the peak in the plot of the transition temperature against the composition to about 479 at% cobalt from the 50 at% predicted by the usual Bragg-Williams theory

M Iwamatsu

Papers

Structures of metallic clusters: Mono- and polyvalent metals

Magnetic susceptibilities of liquid binary alloys

Band theory of the order-disorder transition in iron-cobalt alloys