An Improved Self-Adaptive Differential Evolution with the Neighborhood Search Algorithm for Global Optimization of Bimetallic Clusters.

Global optimization of multicomponent cluster structures is considerably time-consuming due to the existence of a vast number of isomers. In this work, we proposed an improved self-adaptive differential evolution with the neighborhood search (SaNSDE) algorithm and applied it to the global optimization of bimetallic cluster structures. The cross operation was optimized, and an improved basin hopping module was introduced to enhance the searching efficiency of SaNSDE optimization. Taking (PtNi)N (N = 38 or 55) bimetallic clusters as examples, their structures were predicted by using this algorithm. The traditional SaNSDE algorithm was carried out for comparison with the improved SaNSDE algorithm. For all the optimized clusters, the excess energy and the second difference of the energy were calculated to examine their relative stabilities. Meanwhile, the bond order parameters were adopted to quantitatively characterize the cluster structures. The results reveal that the improved SaNSDE algorithm possessed significantly higher searching capability and faster convergence speed than the traditional SaNSDE algorithm. Furthermore, the lowest-energy configurations of (PtNi)38 clusters could be classified as the truncated octahedral and disordered structures. In contrast, all the optimal (PtNi)55 clusters were approximately icosahedral. Our work fully demonstrates the high efficiency of the improved algorithm and advances the development of global optimization algorithms and the structural prediction of multicomponent clusters.

Basin Hopping Genetic Algorithm for Global Optimization of PtCo Clusters.

In general, searching the lowest-energy structures is considerably more time-consuming for bimetallic clusters than for monometallic ones because of the presence of an increasing number of homotops and geometrical isomers. In this article, a basin hopping genetic algorithm (BHGA), in which the genetic algorithm is implanted into the basin hopping (BH) method, is proposed to search the lowest-energy structures of 13-, 38-, and 55-atom PtCo bimetallic clusters. The results reveal that the proposed BHGA, as compared with the standard BH method, can markedly improve the convergent speed for global optimization and the possibility for finding the global minima on the potential energy surface. Meanwhile, referencing the monometallic structures in initializations may further raise the searching efficiency. For all the optimized clusters, both the excess energy and the second difference of the energy are calculated to examine their relative stabilities at different atomic ratios. The bond order parameter, the similarity function, and the shape factor are also adopted to quantitatively characterize the cluster structures. The results indicate that the 13- and the 55-atom systems tend to be icosahedral despite different degrees of lattice distortions. In contrast, for the 38-atom system, Pt10Co28, Pt11Co27, Pt17Co21, Pt19Co19, Pt20Co18, and Pt30Co8 tend to be disordered, while Pt21Co17 presents a defected face-centered cubic (fcc) structure, and the remaining clusters are perfect fcc. The methodology and results of this work have referential significance to the exploration of other alloy clusters.