Paleico Martín Leandro, Behler Jörg
Institut für Physikalische Chemie, Theoretische Chemie, Universität Göttingen, Tammannstraße 6, 37077 Göttingen, Germany.
J Chem Phys. 2020 Mar 7;152(9):094109. doi: 10.1063/1.5142363.
Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore the potential energy surface of the system of interest. These simulations can be very demanding due to the high-dimensional configurational search space. The effective search space can be reduced by utilizing grids for the atomic positions, but at the cost of possibly biasing the results if fixed grids are employed. In this paper, we present a flexible grid algorithm for global optimization that allows us to exploit the efficiency of grids without biasing the simulation outcome. The method is general and applicable to very heterogeneous systems, such as interfaces between two materials of different crystal structures or large clusters supported at surfaces. As a benchmark case, we demonstrate its performance for the well-known global optimization problem of Lennard-Jones clusters containing up to 100 particles. Despite the simplicity of this model potential, Lennard-Jones clusters represent a challenging test case since the global minima for some "magic" numbers of particles exhibit geometries that are very different from those of clusters with only a slightly different size.
全局优化是原子模拟中一个活跃的研究领域，迄今为止已经提出了许多算法。一个突出的例子是盆地跳跃蒙特卡罗算法，它执行一种改进的梅特罗波利斯蒙特卡罗搜索，以探索感兴趣系统的势能面。由于高维构型搜索空间，这些模拟可能要求很高。通过使用原子位置的网格可以减少有效的搜索空间，但如果使用固定网格，可能会以偏向结果为代价。在本文中，我们提出了一种用于全局优化的灵活网格算法，该算法使我们能够利用网格的效率而不偏向模拟结果。该方法具有通用性，适用于非常不均匀的系统，例如具有不同晶体结构的两种材料之间的界面或表面支撑的大团簇。作为一个基准案例，我们展示了它在包含多达100个粒子的著名的 Lennard-Jones 团簇全局优化问题上的性能。尽管这个模型势很简单，但 Lennard-Jones 团簇代表了一个具有挑战性的测试案例，因为对于某些“神奇”粒子数的全局最小值呈现出与尺寸仅略有不同的团簇非常不同的几何形状。
