Yang Wei-Hua, Yu Fang-Qi, Huang Rao, Shao Gui-Fang, Liu Tun-Dong, Wen Yu-Hua
Department of Physics, Xiamen University, Xiamen 361005, China.
Pen-Tung Sah Institute of Micro-Nano Science and Technology, Xiamen University, Xiamen 361005, China.
J Chem Inf Model. 2023 Nov 13;63(21):6727-6739. doi: 10.1021/acs.jcim.3c01331. Epub 2023 Oct 18.
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 Co, Pt, and Fe ( = 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 Fe 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.
确定过渡金属团簇的最优结构并阐明其相应的层级演化对于它们的应用至关重要。然而，对包含大量原子的团簇进行全局优化是物理和化学许多领域中极具挑战性的任务。在这项工作中，采用了一种高效的带邻域搜索的自适应差分进化（SaNSDE）算法，该算法引入了优化的交叉操作和改进的盆地跳跃模块，以搜索Co、Pt和Fe（n = 3 - 200）团簇的最低能量结构。首先通过将我们的结果与剑桥团簇数据库（CCD）中收集的并行结果进行比较来评估SaNSDE算法的性能。随后，引入不同的分析方法来系统地研究这些团簇的结构和能量性质，并特别关注通过探索它们的整体形状、原子排列、结构相似性和生长模式来阐明团簇尺寸与结构演化的关系。与CCD中列出的结果相比，发现了13个能量更低的Fe团簇结构。此外，我们的结果表明，这三种金属的团簇具有不同的幻数和超稳定结构，其中大多数具有高对称性。Co、Pt和Fe团簇的结构演化分别可主要视为闭壳二十面体、马克斯十面体和无序二十面体环生长。此外，发现了壳层结构的形成，并确定了具有hcp -、fcc -和bcc - 类构型的团簇。然而，尽管配位数逐渐向其体相极限饱和，但团簇的生长并非简单地在给定团簇上逐个原子堆积。我们的工作确定了如此广泛团簇尺寸区域的一般生长趋势，这在第一性原理计算中成本高得难以承受，并推动了用于团簇结构预测的全局优化算法的发展。
