Diversity driven unbiased search of minimum energy cluster configurations

Abstract

The determination of the spatial distributions that atoms adopt to form condensed matter is a problem of crucial importance, since most physical properties depend on the atomic arrangement. This is especially relevant for clusters, where periodicity is nonexistent. Several optimization procedures have been implemented to tackle this problem, with ever increasing success. Here we put forward a search scheme which preserves as large a diversity as allowed by the use of phenomenological potentials, generating in an unbiased fashion a bank of configurations to be explored; a procedure we denominate diversity driven unbiased search (DDUS). It consists in the generation, using phenomenological potentials, of a data bank of putative minima rather than a single, or just a few, configurations which are based on the conformational space annealing method (CSA). All of the configurations in the bank are thereafter refined by means of DFT computations. Certainly, in spite of our efforts to generate a bank as diverse as possible, not all relevant structures might be included in it, since quantum effects are ignored. The procedure is applied to several examples of rhodium, palladium, silver, platinum and gold clusters, between 5 and 23 atoms in size. The main conclusion we reach is that unbiased search, among a significant number of candidates, quite often leads to rather unexpectedly low symmetry configurations, which turn out to be the lowest energy ones within our scheme.

Analyzing the properties of clusters: Structural similarity and heat capacity

“…Also Rogan et al [13] introduced a quantity that should quantify the similarity between two clusters of the same size. In this case, only a single number, related to the moments of inertia, is used for each structure.…”

A study on diversity for cluster geometry optimization

“…RMSD is not considered in our analysis since is it not usually applied to estimate dissimilarity in cluster geometry optimization problems. For completeness, one can also refer the measures proposed by Grigoryan et al [13] and Rogan et al [40], which can be considered as variants respectively of structural and center of mass distances.…”

A strategy to find minimal energy nanocluster structures

“…Practically, all physical properties depend on its structure." During the last years, a variety of techniques such as Monte Carlo, [2,3] Big-Bang, [4] genetic algorithm (GA), [5][6][7] conformational space annealing, [8][9][10] Basin Hopping (BH), [11] among others, have been used to determine minimum energy cluster configurations, with varying degree of success. Many variations and alternative procedures have been put forward, like the one by Goedecker [12] who focuses on obtaining the global minimum by means of an interesting and ingenious method, which reduces repeated visits to the same attraction basin by "flooding" it.…”