PDECO: parallel differential evolution for clusters optimization

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.