Global Optimization of Li and Na Clusters: Application of a Modified Embedded Atom Method

Abstract

An analytic modified embedded atom method (MEAM), developed for bulk alkali metals, is used to identify up to six different, energetically lowest isomers of $$\hbox {Li}_N$$ and $$\hbox {Na}_N$$ clusters (N = 2 − 150) within an unbiased global structure-optimization procedure. Randomly generated clusters are locally optimized using the quasi-Newton method and the resulting six most stable isomers are used afterwards in the Aufbau–Abbau algorithm. Due to its analytical formulae and its semiempirical nature, the MEAM emerges as a fast and efficient method that is particularly suitable for an unbiased global optimization. Structural and energetic analyses show that the MEAM provides compact clusters that are in good agreement with the results of other semiempirical calculations. Occasionally, the MEAM produces structures that are normally not found with such model potentials but in more accurate DFT or ab initio studies. Moreover, clusters of pronounced stability (magic sizes) are identified, growth patterns are studied, and trends can be recognized in which the atomic arrangement within the clusters of the considered size range corresponds more to the fcc than to the bcc packing. Additionally, for most cluster sizes the structures of the lowest-energy isomers of $$\hbox {Li}_N$$ and $$\hbox {Na}_N$$ clusters are very similar.