Comprehensive genetic algorithm forab initioglobal optimisation of clusters

Abstract

Cluster, as the aggregate of a few to thousands of atoms or molecules, bridges the microscopic world of atoms and molecules and the macroscopic world of condensed matters. The physical and chemical properties of a cluster are determined by its ground state structure, which is significantly different from its bulk structure and sensitively relies on the cluster size. As a well-known nondeterministic polynomial-time hard problem, determining the ground state structure of a cluster is a challenging task due to the extreme complexity of high-dimensional potential energy surface (PES). Genetic algorithm (GA) is an efficient global optimisation method to explore the PES of clusters. Recently, we have developed a GA-based programme, namely comprehensive genetic algorithm (CGA), and incorporated it with ab initio calculations. Using this programme, the lowest energy structures of a variety of elemental and compound clusters with different types of chemical bonding have been determined, and their physical properties have been investigated and compared with experimental data. In this article, we will describe the technique details of CGA programme and present an overview of its successful applications.

Hydrated Sodium Ion Clusters [Na+(H2O)n (n = 1–6)]: An ab initio Study on Structures and Non-covalent Interaction

“…In this work, some of the structures of the Na + (H 2 O) n ( n = 1–6) clusters are adopted from previous literatures (Bauschlicher et al, 1991; Glendening and Feller, 1995; Ke et al, 2015; Fifen and Agmon, 2016). To obtain more isomers for n = 4–6, a global search with the comprehensive genetic algorithm (CGA, Zhao et al, 2016) combined with DMol 3 program (Delley, 2000) based on DFT was executed. The CGA method is described in our previous review in detail (Zhao et al, 2016).…”

“…To obtain more isomers for n = 4–6, a global search with the comprehensive genetic algorithm (CGA, Zhao et al, 2016) combined with DMol 3 program (Delley, 2000) based on DFT was executed. The CGA method is described in our previous review in detail (Zhao et al, 2016). For each cluster size with n ≥ 4, we took 10 independent global searches, and for each search, we maintained mating and mutation operations on a population of eight members of up to 3000 GA iterations.…”

Revisit of large‐gap Si16 clusters encapsulating group‐IV metal atoms (Ti, Zr, Hf)

“…The low‐energy structures of neutral and anionic M@Si 16 clusters (M = Ti, Zr, and Hf) were globally searched using our self‐developed comprehensive genetic algorithm (CGA) incorporated into an all‐electron DFT program, i.e., DMol 3 . The essential details of the CGA code can be found in our recent review . For each cluster, independent GA search was performed using at least 3000 iterations retaining 16 members in the population.…”

First-Principles Studies on the Structural and Electronic Properties of As Clusters

“…In order to search the global minimum structures of As n clusters, we combined a genetic algorithm (GA) simulation with local optimization at the Dmol 3 level [24,25,26,27,28,29]. The fundamental aim in GA is to divide the potential-energy surface (PES) into a number of regions and find the locally stable isomers in each region.…”