A strategy to find minimal energy nanocluster structures

Abstract

An unbiased strategy to search for the global and local minimal energy structures of free standing nanoclusters is presented. Our objectives are twofold: to find a diverse set of low lying local minima, as well as the global minimum. To do so, we use massively the fast inertial relaxation engine algorithm as an efficient local minimizer. This procedure turns out to be quite efficient to reach the global minimum, and also most of the local minima. We test the method with the Lennard-Jones (LJ) potential, for which an abundant literature does exist, and obtain novel results, which include a new local minimum for LJ13 , 10 new local minima for LJ14 , and thousands of new local minima for 15≤N≤65. Insights on how to choose the initial configurations, analyzing the effectiveness of the method in reaching low-energy structures, including the global minimum, are developed as a function of the number of atoms of the cluster. Also, a novel characterization of the potential energy surface, analyzing properties of the local minima basins, is provided. The procedure constitutes a promising tool to generate a diverse set of cluster conformations, both two- and three-dimensional, that can be used as an input for refinement by means of ab initio methods.

Theoretical determination of the differential polarizability and anisotropy of alkaline earth oxide nanoclusters (BeO)n[n= 2-9]: The basis set and electron correlation effects

“…After global optimization, the low‐lying isomers are fully relaxed at TPSSh/6‐311+G(d) level of theory . For more details on the global optimization algorithms of clusters, we refer the reader to some recent reviews in this context …”

“…[13] For more details on the global optimization algorithms of clusters, we refer the reader to some recent reviews in this context. [24,25] FULL PAPER Relying on the established structures for beryllium oxide clusters, in the present work, we optimized the geometries of BeO clusters which build up by 4 to 18 atoms. Shown in Figure 1 is the lowest energy structure of (BeO) n clusters with 2 n 9 optimized at the TPSSh/6-3111G(d) level of theory.…”

Structural, electronic, and magnetic properties of Fe Co Ni (x+y+z=13) clusters: A density-functional-theory study

“…After this minimization process, we kept only the conformations that are truly different, since due to symmetry and atomic indistinguishability many homotops are equivalent. This particular minimization process, using phenomenological potentials, has been introduced in a recent publication by Rogan et al [14], and has been successfully implemented in several recent publications [36][37][38]. We keep only the lowest energy configurations, for a given structure and (x y z , , ) values, and perform a reoptimization using the SIESTA code.…”

“…The number of energy minima of 13 atom homonuclear clusters is large indeed: for example, if one uses a Lennard-Jones phenomenological potential 1510 different minimal conformations have been found [14]. When dealing with alloys, even just binary ones, the challenge becomes significantly more arduous, because of the many ways the different atomic species can be arranged in a cluster, which increases enormously the number of possible configurations in relation to pristine samples.…”

Multibody expansion of particle interactions: How many-body is a particular element in a cluster

“…However, the complexity of the problem is quite overwhelming as can easily be perceived by pointing out that a 13-atom cluster, interacting via a simple Lennard-Jones two-body potential, has a potential energy surface function with around 1000 minima [3]. Even more impressive is that for a 147-atom cluster this number grows to ∼10 50 minima [4].…”