Clever and Efficient Method for Searching Optimal Geometries of Lennard-Jones Clusters

Abstract

An unbiased algorithm for determining global minima of Lennard-Jones (LJ) clusters is proposed in the present study. In the algorithm, a global minimum is searched by using two operators: one modifies a cluster configuration by moving atoms to the most stable positions on the surface of a cluster and the other gives a perturbation on a cluster configuration by moving atoms near the center of mass of a cluster. The moved atoms are selected by employing contribution of the atoms to the potential energy of a cluster. It was possible to find new global minima for LJ506, LJ521, LJ536, LJ537, LJ538, and LJ541 together with putative global minima of LJ clusters of 10-561 atoms reported in the literature. This indicates that the present method is clever and efficient for cluster geometry optimization.

Binary Lennard-Jones atomic clusters: Structural features induced by large-sized atoms

“…Previously the present author developed an efficient method for geometry optimization of Lennard-Jones clusters [10]. The method optimizes cluster geometries with two types of geometrical perturbations and yielded the global minima of LJ clusters with 10 to 561 atoms reported previously and the new minima for 6 LJ clusters.…”

“…In the previous study on the LJ clusters by the present author [10], two geometrical perturbations followed by local optimizations efficiently explore geometrical space. For the BLJ clusters, the atom types must be taken into account in the optimization algorithm.…”

“…A simple way to optimize the type of the atom is to convert A into B or vice versa in the algorithm as performed in the literature [18]. In the present study, an optimization method was developed by combination of the two perturbations [10] with the atom-type conversion [18] algorithm. To evaluate the combined method, geometry optimization was performed for the BLJ 5 to BLJ 100 for s = 1.05, 1.1, 1.15, 1.2, 1.25, 1.3.…”

Empirical Review of Standard Benchmark Functions Using Evolutionary Global Optimization

“…Chemical structure optimization of clusters is an obvious example: Of central practical importance are phenomena like cluster aggregation and fragmentation, or the dependence of properties on cluster size, while isolating a single cluster size is a formidable experimental challenge. Therefore, one does not study a single cluster size but tries to systematically study a range of clusters [8,9,[17][18][19], only limited by the maximum computing capacity one has. It is obvious that smallest decreases in scaling (e.g.…”

The structural investigation on small methane clusters described by two different potentials

“…The present author proposed an efficient geometry optimization method for atomic/molecular clusters (the Heuristic Method combined with Geometrical Perturbations, HMGP) [27,28]. In this work, the geometries of the methane clusters (CH 4 ) n with n ≤ 40 expressed by two different interatomic potentials are optimized with HMGP and geometrical features of the clusters are reported.…”