Kanayama Kansei, Seko Atsuto, Toyoura Kazuaki
Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan.
Phys Rev E. 2023 Sep;108(3-2):035303. doi: 10.1103/PhysRevE.108.035303.
The Dividing Rectangles (DIRECT) algorithm is a deterministic optimization method to explore optimal solutions by repeatedly dividing a given hyperrectangle search space into subhyperrectangles. Herein, we propose a structure search method for atomic clusters based on the DIRECT algorithm in combination with a gradient-based local optimizer to enable an efficient structure search in high-dimensional search spaces. We use the Z-matrix representation for defining the hyperrectangle search space, in which the bond lengths, bond angles, and dihedral angles specify a cluster structure. To evaluate its performance, we applied the proposed method to the Lennard-Jones clusters and two kinds of real atomic clusters with many metastable structures, i.e., phosphorus and sulfur clusters, and compared the results with those of conventional methods. The proposed method exhibits a higher efficiency than random search and a comparable efficiency to basin hopping.
划分矩形（DIRECT）算法是一种确定性优化方法，通过将给定的超矩形搜索空间反复划分为子超矩形来探索最优解。在此，我们提出了一种基于DIRECT算法并结合基于梯度的局部优化器的原子簇结构搜索方法，以在高维搜索空间中实现高效的结构搜索。我们使用Z矩阵表示来定义超矩形搜索空间，其中键长、键角和二面角指定了簇结构。为了评估其性能，我们将所提出的方法应用于 Lennard-Jones 簇以及具有许多亚稳结构的两种真实原子簇，即磷簇和硫簇，并将结果与传统方法的结果进行了比较。所提出的方法比随机搜索具有更高的效率，并且与盆地跳跃法具有相当的效率。
