Application of Optimization Algorithms in Clusters

Abstract

The structural characterization of clusters or nanoparticles is essential to rationalize their size and composition-dependent properties. As experiments alone could not provide complete picture of cluster structures, so independent theoretical investigations are needed to find out a detail description of the geometric arrangement and corresponding properties of the clusters. The potential energy surfaces (PES) are explored to find several minima with an ultimate goal of locating the global minima (GM) for the clusters. Optimization algorithms, such as genetic algorithm (GA), basin hopping method and its variants, self-consistent basin-to-deformed-basin mapping, heuristic algorithm combined with the surface and interior operators (HA-SIO), fast annealing evolutionary algorithm (FAEA), random tunneling algorithm (RTA), and dynamic lattice searching (DLS) have been developed to solve the geometrical isomers in pure elemental clusters. Various model or empirical potentials (EPs) as Lennard–Jones (LJ), Born–Mayer, Gupta, Sutton–Chen, and Murrell–Mottram potentials are used to describe the bonding in different type of clusters. Due to existence of a large number of homotops in nanoalloys, genetic algorithm, basin-hopping algorithm, modified adaptive immune optimization algorithm (AIOA), evolutionary algorithm (EA), kick method and Knowledge Led Master Code (KLMC) are also used. In this review the optimization algorithms, computational techniques and accuracy of results obtained by using these mechanisms for different types of clusters will be discussed.

Optimizing the Shape and Chemical Ordering of Nanoalloys with Specialized Walkers

“…[22] Even focusing on the study of the global optimization of metal nanoparticles and nanoalloys only, there has been intense research activity and much effort, because of the importance of these systems both in fundamental science and in practical applications. [23][24][25][26][27] Different methods have been recently developed to tackle the problem of global optimization: basin hopping [28] and evolutionary-based algorithms, [29][30][31][32][33][34][35][36][37] lattice Monte Carlo, [38] mirror-rotation optimization algorithms, [39] curvilinear coordinate, [40] biminima optimizations, [41,42] and particle swarm optimization. [43] Global optimization is a very challenging task already for one-component (elemental) nanoparticles due to the enormous number of local equilibrium configurations (i.e., of local minima) of the PES, which is expected to exponentially increase with the number of atoms N. [44][45][46] These local minima correspond to different geometric structures which in principle can present quite different properties.…”

Monte Carlo-Simulated Annealing and Machine Learning-Based Funneled Approach for Finding the Global Minimum Structure of Molecular Clusters

“…31 This article is licensed under CC-BY-NC-ND 4 Most gas-phase cluster algorithms usually contain two main steps: the first involves identifying local minima on the PES using low-cost energy calculations. There are a variety of methods for minima search on the PES, including genetic algorithms (GA), 8−13 Monte Carlo simulations (MC), 8,9 and molecular dynamics simulations (MD). 8,9 The second step is usually a geometry optimization of the low-lying isomers found on the PES using higher level scoring methods, such as quantum chemistry calculations.…”

“…Moreover, in the gas phase, in contrast to the solid state, the clusters are not limited by any known symmetry groups or sizes. Many different algorithms have been used to tackle the problem of clusters in the gas phase. − A well-known algorithm for periodic systems is the ab initio random structure searching (AIRSS) . The algorithm generates random “sensible” structures and then relaxes them into the closest minimum point using periodic DFT, possibly using symmetries to help to narrow down the search space.…”

Atomic Clusters: Structure, Reactivity, Bonding, and Dynamics

“…Various experimental techniques such as laser ablation coupled with mass spectrometry, photoelectron spectroscopy have been employed to get insights into the atomic clusters. Along with experimental studies, theoretical investigations are required to get a better understanding of their geometric arrangement and corresponding properties (Srivastava, 2021).…”