Global optimization of chemical cluster structures: Methods, applications, and challenges

Abstract

Chemical clusters are relevant to many applications in catalysis, separations, materials, and energy sciences. Experimentally, the structure of clusters is difficult to determine, but it is very important in understanding their chemistry and properties. Computational methods can be used to examine cluster structure, however finding the most stable structure is not simple, particularly as the cluster size increases. Global optimization techniques have long been used to tackle the problem of the most stable structure, but such approaches would have to look for a global minimum, while sampling local minima over the whole potential energy surface as well. In this review, the state‐of‐the‐art theory of global optimization theory is summarized. First, the definition, significance, relation to experiments, and a brief history of global optimization is presented. We then discuss, in more detail, three versatile global optimization methods: the basin hopping, the artificial bee colony algorithm, and the genetic algorithm. We close with some representative application examples of global optimization of clusters since 2016 and the challenges, open questions and opportunities in this field.

Free Energies of Hydrated Halide Anions: High Through-Put Computations on Clusters to Treat Rough Energy-Landscapes

“…The assumption of harmonic motion is valid for clusters with strong interactions that limit atomic displacements to small distances away from an optimized geometry [ 27 ]. A challenge common to harmonic and anharmonic estimates of the free energy is that more than one low energy structure may be relevant [ 28 , 29 , 30 ]. Similar to earlier results found for simple cations [ 28 , 31 ], harmonic approximations ( Figure 1 ) are satisfactory for W F and , but not for in that case.…”

Search for Global Minimum Structures of P2n+1+ (n = 1–15) Using xTB-Based Basin-Hopping Algorithm

“…The BH algorithm was then applied for the selected isomers based on their energies after the xTB optimization. Considering the BH method is one of the individual-based methods ( Zhang and Glezakou, 2020 ), an initialized population with suitable size is applied here to improve its performance in the global optimization. After the selection of initial seed structures for BH algorithm based on their energies calculated by the xTB method, distorted structures are generated from the seeds by the displacement.…”

“…There are many wonderful examples, including the cage-like fused-ring structure (truncated icosahedron) of C 60 fullerene ( Kroto et al, 1985 ), the tetrahedral structure of Au 20 ( Li et al, 2003 ), C 6v symmetry boron cluster of B 36 ( Piazza et al, 2014 ), the borospherene cluster of B 40 ( Zhai et al, 2014 ; Li et al, 2017 ), and the protonated serine octamer ( Cooks et al, 2001 ; Kong et al, 2006 ; Scutelnic et al, 2018 ). In lots of cases, the structural information of the clusters can hardly be obtained directly from experiments, and theoretical calculations are very important to provide structural candidates whose predicted properties should be further compared with the experimental results, in order to make the identification stable ( Zhang and Glezakou, 2020 ).…”

“…Since the numbers of local minima grow quickly with the size of clusters, the global optimization becomes a very difficult task to overcome. Thus, different search algorithms and methodologies, including the genetic algorithm (GA) ( Hartke, 1993 ; Deaven and Ho, 1995 ; Hartke, 1995 ; Daven et al, 1996 ; Rogan et al, 2013 ; Kanters and Donald, 2014 ; Shayeghi et al, 2015 ; Lazauskas et al, 2017 ; Rabanal-León et al, 2018 ; Jäger et al, 2019 ; Yañez et al, 2019 ) and relative evolutionary algorithm (EA) ( Zhou et al, 2020 ), the swarm intelligence algorithm ( Wang et al, 2012 ; Jana et al, 2019 ) and others, have been proposed and applied in the past decades ( Zhang and Glezakou, 2020 ).…”

Dynamics of Heterogeneous Catalytic Processes at Operando Conditions

“… 46 This concept is the so-called “dynamic fluxionality”, which implies that the single structure obtained from the GO algorithm represents the most abundant isomer in the ensemble of structures. 44 …”