Structural Determination and Hierarchical Evolution of Transition Metal Clusters Based on an Improved Self-Adaptive Differential Evolution with Neighborhood Search Algorithm.

Determining the optimal structures and clarifying the corresponding hierarchical evolution of transition metal clusters are of fundamental importance for their applications. The global optimization of clusters containing a large number of atoms, however, is a vastly challenging task encountered in many fields of physics and chemistry. In this work, a high-efficiency self-adaptive differential evolution with neighborhood search (SaNSDE) algorithm, which introduced an optimized cross-operation and an improved Basin Hopping module, was employed to search the lowest-energy structures of CoN, PtN, and FeN (N = 3-200) clusters. The performance of the SaNSDE algorithm was first evaluated by comparing our results with the parallel results collected in the Cambridge Cluster Database (CCD). Subsequently, different analytical methods were introduced to investigate the structural and energetic properties of these clusters systematically, and special attention was paid to elucidating the structural evolution with cluster size by exploring their overall shape, atomic arrangement, structural similarity, and growth pattern. By comparison with those results listed in the CCD, 13 lower-energy structures of FeN clusters were discovered. Moreover, our results reveal that the clusters of three metals had different magic numbers with superior stable structures, most of which possessed high symmetry. The structural evolution of Co, Pt, and Fe clusters could be, respectively, considered as predominantly closed-shell icosahedral, Marks decahedral, and disordered icosahedral-ring growth. Further, the formation of shell structures was discovered, and the clusters with hcp-, fcc-, and bcc-like configurations were ascertained. Nevertheless, the growth of the clusters was not simply atom-to-atom piling up on a given cluster despite gradual saturation of the coordination number toward its bulk limit. Our work identifies the general growth trends for such a wide region of cluster sizes, which would be unbearably expensive in first-principles calculations, and advances the development of global optimization algorithms for the structural prediction of clusters.

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.

Modelling free and oxide-supported nanoalloy catalysts: comparison of bulk-immiscible Pd-Ir and Au-Rh systems and influence of a TiO2 support.

The relative stabilities of different chemical arrangements of Pd-Ir and Au-Rh nanoalloys (and their pure metal equivalents) are studied, for a range of compositions, for fcc truncated octahedral 38- and 79-atom nanoparticles (NPs). For the 38-atom NPs, comparisons are made of pure and alloy NPs supported on a TiO2(110) slab. The relative energies of different chemical arrangements are found to be similar for Pd-Ir and Au-Rh nanoalloys, and depend on the cohesive and surface energies of the component metals. For supported nanoalloys on TiO2, the interaction with the surface is greater for Ir (Rh) than Pd (Au): most of the pure NPs and nanoalloys preferentially bind to the TiO2 surface in an edge-on configuration. When Au-Rh nanoalloys are bound to the surface through Au, the surface binding strength is lower than for the pure Au NP, while the Pd-surface interaction is found to be greater for Pd-Ir nanoalloys than for the pure Pd NP. However, alloying leads to very little difference in Ir-surface and Rh-surface binding strength. Comparing the relative stabilities of the TiO2-supported NPs, the results for Pd-Ir and Au-Rh nanoalloys are the same: supported Janus NPs, whose Ir (Rh) atoms bind to the TiO2 surface, bind most strongly to the surface, becoming closer in energy to the core-shell configurations (Ir@Pd and Rh@Au) which are favoured for the free particles.

DFT study of the structure, chemical ordering and molecular adsorption of Pd-Ir nanoalloys.

The structures and surface adsorption sites of Pd-Ir nanoalloys are crucial to the understanding of their catalytic performance because they can affect the activity and selectivity of nanocatalysts. In this article, density functional theory (DFT) calculations are performed on bare Pd-Ir nanoalloys to systematically explore their stability and chemical ordering properties, before studying the adsorption of CO on the nanoalloys. First, the structural stability of 38-atom and 79-atom truncated octahedral (TO) Pd-Ir nanoalloys are investigated. Then the adsorption properties and preferred adsorption sites of CO on 38-atom Pd-Ir nanoalloys are considered. The PdshellIrcore structure, which has the lowest energy of all the considered isomers, exhibits the highest structural stability, while the PdcoreIrshell configuration is the least stable. In addition, the adsorption strength of CO on Ir atoms is found to be greater than on Pd for Pd-Ir nanoclusters. The preferred adsorption sites of CO on pure Pd and Ir clusters are in agreement with calculations and experiments on extended Pd and Ir surfaces. In addition, d-band center and charge effects on CO adsorption strength on Pd-Ir nanoalloys are analyzed by comparison with pure clusters. The study provides a valuable theoretical insight into catalytically active Pd-Ir nanoalloys.

Hierarchical structures and magnetism of Co clusters: a perspective from integration of deep learning and a hybrid differential evolution algorithm.

Theoretically determining the lowest-energy structure of a cluster has been a persistent challenge due to the inherent difficulty in accurate description of its potential energy surface (PES) and the exponentially increasing number of local minima on the PES with the cluster size. In this work, density-functional theory (DFT) calculations of Co clusters were performed to construct a dataset for training deep neural networks to deduce a deep potential (DP) model with near-DFT accuracy while significantly reducing computational consumption comparable to classic empirical potentials. Leveraging the DP model, a high-efficiency hybrid differential evolution (HDE) algorithm was employed to search for the lowest-energy structures of CoN (N = 11-50) clusters. Our results revealed 38 of these clusters superior to those recorded in the Cambridge Cluster Database and identified diverse architectures of the clusters, evolving from layered structures for N = 11-27 to Marks decahedron-like structures for N = 28-42 and to icosahedron-like structures for N = 43-50. Subsequent analyses of the atomic arrangement, structural similarity, and growth pattern further verified their hierarchical structures. Meanwhile, several highly stable clusters, i.e., Co13, Co19, Co22, Co39, and Co43, were discovered by the energetic analyses. Furthermore, the magnetic stability of the clusters was verified, and a competition between the coordination number and bond length in affecting the magnetic moment was observed. Our study provides high-accuracy and high-efficiency prediction of the optimal structures of clusters and sheds light on the growth trend of Co clusters containing tens of atoms, contributing to advancing the global optimization algorithms for effective determination of cluster structures.