PDECO: Parallel differential evolution for clusters optimization

Abstract

The optimization of the atomic and molecular clusters with a large number of atoms is a very challenging topic. This article proposes a parallel differential evolution (DE) optimization scheme for large-scale clusters. It combines a modified DE algorithm with improved genetic operators and a parallel strategy with a migration operator to address the problems of numerous local optima and large computational demanding. Results of Lennard-Jones (LJ) clusters and Gupta-potential Co clusters show the performance of the algorithm surpasses those in previous researches in terms of successful rate, convergent speed, and global searching ability. The overall performance for large or challenging LJ clusters is enhanced significantly. The average number of local minimizations per hit of the global minima for Co clusters is only about 3-4% of that in previous methods. Some global optima for Co are also updated. We then apply the algorithm to optimize the Pt clusters with Gupta potential from the size 3 to 130 and analyze their electronic properties by density functional theory calculation. The clusters with 13, 38, 54, 75, 108, and 125 atoms are extremely stable and can be taken as the magic numbers for Pt systems. It is interesting that the more stable structures, especially magic-number ones, tend to have a larger energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital. It is also found that the clusters are gradually close to the metal bulk from the size N > 80 and Pt38 is expected to be more active than Pt75 in catalytic reaction.

What are grain boundary structures in graphene?

“…[36][37][38][39][40] In the basic DE algorithm, each solution candidate is treated as a vector in the D-dimensional phase space, and involves in three steps: mutation, crossover and selection. The mutation operation generates a mutant vector v for the ith target vector x in the population as follow:…”

NWPEsSe: an Adaptive-Learning Global Optimization Algorithm for Nanosized Cluster Systems

“…Eq. 6has been proven to be highly efficient in exchanging information between individuals of a population in swarm-intelligencebased algorithms, 33,34,43,88 introducing multiple interactions between individuals. This is a random exploration of cluster structures.…”

“…Examples of global optimization algorithms used on a variety of systems (aperiodic or periodic) have been reported in the literature and include Li , 37 Ir , 38 Pt , 39 graphene-supported Pt , 40 MgOsupported AuPd, 41 TiCl 4 -capped MgCl 2 plate (Ziegler-Natta catalyst), 42 to name a few. Other general-purpose codes include PDECO, 43 GEGA, 37 GMIN, 44 TGMIN, 45 AUTOMATON, 46 etc. However, some of these codes are either not readily available, lack the interface to common computational chemistry programs, or are simply designed for specific systems.…”

Inverse design of materials by multi-objective differential evolution

“…Greedy strategy is taken by the algorithm only keeping new candidates which out-perform the old ones. The evolutionary nature of the DE algorithm makes it a very effective solver for complex search problems, including either global or multi-objective problems, have already been applied for structure searching of cluster and interface [25,26]. Therefore MODE algorithm is suitable to be applied to the inverse material design problem.…”