Exploring the MP2 energy surface of nanoalloy clusters with a genetic algorithm: Application to sodium–potassium

Modeling microsolvation clusters with electronic-structure calculations guided by analytical potentials and predictive machine learning techniques

We propose a new methodology to study, at the density functional theory (DFT) level, the clusters resulting from the microsolvation of alkali-metal ions with rare-gas atoms. The workflow begins with a global optimization search to generate a pool of low-energy minimum structures for different cluster sizes. This is achieved by employing an analytical potential energy surface (PES) and an evolutionary algorithm (EA). The next main stage of the methodology is devoted to establish an adequate DFT approach to treat the microsolvation system, through a systematic benchmark study involving several combinations of functionals and basis sets, in order to characterize the global minimum structures of the smaller clusters. In the next stage, we apply machine learning (ML) classification algorithms to predict how the low-energy minima of the analytical PES map to the DFT ones. An early and accurate detection of likely DFT local minima is extremely important to guide the choice of the most promising low-energy minima of large clusters to be re-optimized at the DFT level of theory. In this work, the methodology was applied to the Li+Krn (n = 2-14 and 16) microsolvation clusters for which the most competitive DFT approach was found to be the B3LYP-D3/aug-pcseg-1. Additionally, the ML classifier was able to accurately predict most of the solutions to be re-optimized at the DFT level of theory, thereby greatly enhancing the efficiency of the process and allowing its applicability to larger clusters.

Application of a quantum genetic algorithm and QTAIM analysis in the study of structural and electronic properties of neutral bimetallic clusters NaxLiy (4 ≤ x + y ≤ 10)

Alloy clusters of Na_xLi_y (4 ≤ x + y ≤ 10) are studied by exploring the potential energy surface in the ab initio MP2 level with the support of a quantum genetic algorithm (QGA). In some cases, the structures have been also refined with DFT and coupled-cluster methods. The general trends of sodium-lithium structures are in line with previous studies. The ionization potentials and polarizabilities to all structures were calculated with MP2 method and the average error between these two properties compared with experimental data was 6% and 13%, respectively. The topological analysis based on quantum theory of atoms in molecules (QTAIM) showed that by increasing the cluster size of the diatomic system there was a decrease of atomic interaction energies. The degree of degeneracy from D3BIA aromaticity index and the analysis of the atomic charges showed the influence (by charge transfer) of the chemical element in lower quantity in the cluster with respect to the other atoms. Our achievements of comparing our theoretical results with available experimental data have demonstrated that our approach can also predict satisfactorily quantum atomic and alloy clusters properties, at least, for low nuclearities.

Reliability of semiempirical and DFTB methods for the global optimization of the structures of nanoclusters

In this work, we explore the possibility of using computationally inexpensive electronic structure methods, such as semiempirical and DFTB calculations, for the search of the global minimum (GM) structure of chemical systems. The basic prerequisite that these inexpensive methods will need to fulfill is that their lowest energy structures can be used as starting point for a subsequent local optimization at a benchmark level that will yield its GM. If this is possible, one could bypass the global optimization at the expensive method, which is currently impossible except for very small molecules. Specifically, we test our methods with clusters of second row elements including systems of several bonding types, such as alkali, metal, and covalent clusters. The results reveal that the DFTB3 method yields reasonable results and is a potential candidate for this type of applications. Even though the DFTB2 approach using standard parameters is proven to yield poor results, we show that a re-parametrization of only its repulsive part is enough to achieve excellent results, even when applied to larger systems outside the training set.

A method for predicting basins in the global optimization of nanoclusters with applications to AlxCuy alloys

The problem of obtaining the geometrical configuration of a molecule that minimizes its potential energy is a very complicated one for a series of applications, ranging from determining the structure of biological macromolecules to nanoclusters of atoms. Global optimization tools are available for this task, and many of them are based in performing successive local optimizations, where the starting geometries for these steps are determined by an intelligent algorithm. Here we develop a method to save computing time in the optimization of nanoclusters by predicting if a given minimum has been previously visited during local optimization steps. Our application to Cu-Al nanoalloys indicates that it is possible to save a substantial amount of computational cost. The application also reveals new promising Al_xCu_y clusters and explain their stabilities in terms of the jellium model.

A New Genetic Algorithm Approach Applied to Atomic and Molecular Cluster Studies

A new procedure is suggested to improve genetic algorithms for the prediction of structures of nanoparticles. The strategy focuses on managing the creation of new individuals by evaluating the efficiency of operators (o₁, o₂,…,o₁₃) in generating well-adapted offspring. This is done by increasing the creation rate of operators with better performance and decreasing that rate for the ones which poorly fulfill the task of creating favorable new generation. Additionally, several strategies (thirteen at this level of approach) from different optimization techniques were implemented on the actual genetic algorithm. Trials were performed on the general case studies of 26 and 55-atom clusters with binding energy governed by a Lennard-Jones empirical potential with all individuals being created by each of the particular thirteen operators tested. A 18-atom carbon cluster and some polynitrogen systems were also studied within REBO potential and quantum approaches, respectively. Results show that our management strategy could avoid bad operators, keeping the overall method performance with great confidence. Moreover, amongst the operators taken from the literature and tested herein, the genetic algorithm was faster when the generation of new individuals was carried out by the twist operator, even when compared to commonly used operators such as Deaven and Ho cut-and-splice crossover. Operators typically designed for basin-hopping methodology also performed well on the proposed genetic algorithm scheme.

Structural and homotop optimization of neutral Al–Si nanoclusters

The geometry and stability of aluminum–silicon alloys up to 13 atoms are investigated using electronic structure methods.

Structure and stability of neutral Al–Mg nanoclusters up to 55 atoms

The geometries of aluminum–magnesium nanoalloys are explored using a genetic algorithm tuned to search for the 10 lowest energy minima for each cluster size and composition.