Estudo de clusters metálicos de alumínio-sódio, alumíniopotássio, alumínio-lítio e sódio-lítio pelas abordagens de algoritmos genéticos, cálculos quânticos e análise topológica

Abstract

The theoretical study of metal clusters has drawn considerable interest due to the possibility of creating new alloys from materials in nanoscale, the so-called "nanoalloys". Research on nanoalloys has had an important role in materials science, since, among some of its most relevant objectives, we may find the prediction of stability in structures, their manners of growth and further assistance in the interpretation of spectroscopic and other experimental measures. In this context, several methods have been reported in the last few years towards the global minimum optimization of atomic and molecular groups, where the Genetic Algorithm (henceforth GA) is currently considered one of the most used methods, whilst based on principles related to evolutionary processes as well as operators inspired by the Theory of Evolution and Genetics, i. e., by recombination, mutation and natural selection. The GA method in particular, and altogether with the implementation of the Gupta potential, has become efficient in the search for “optimal” solutions for optimization problems in metallic clusters. The present dissertation is composed of chapters consisting of introduction, methodology and theoretical considerations (Chap. 1, 2 and 3), as well as of chapters containing articles on the proposed subject (Chap. 4, 5 and 6). In the first article (Chap. 4), we may find the analysis of AlxNay (x + y ≤ 55) bimetallic clusters through the Genetic Algorithm method with the implementation of the Gupta potential. Also based on the GA application, in the following chapter (Chap. 5) we may find a study regarding AlxLiy e AlxKy (x+y ≤ 55) clusters. In both works, in order to improve GA efficiency, two additional operators have been introduced: Annihilator and History. By being compared to structures obtained by means of GA with Gupta potential for pure aluminum, pure lithium and aluminum-lithium clusters in recent results from literature, it has been verified that, regarding systems Al2, Al3, Al6, Al8, Al9, Li5, Li6, Li7, Al1Li5, Al1Li7 e Al1Li8, the obtained geometries were very similar to those resulting from density functional and ab initio calculations [such as CCSD(T)]. In the third chapter (Chap. 6), we analyzed a new quantum genetic algorithm (QGA) for small cluster systems NaxLiy with (x+y ≤ 10). It has been observed that Q-GA presents an improved efficiency towards a global minimum regarding the GA with the Gupta potential. That has been the case since the former uses the quantum method, while the latter uses a classic method. More specifically, the Q-GA has a narrower scope. In this article, besides ab initio calculations, topological calculations were performed as well, grounded on the Quantum Theory of Atoms in Molecules (QTAIM) for the structures Na1Li5, Na2Li4, Na3Li3, Na4Li2 e Na5Li1 obtained by the Q-GA. In these structures, it is evident that there is no bonding path between the metals, since they are bonded by pseudo atoms, with the exception of the Na5Li1. Some of the atomic interactions have not been suggested by the bonding path, being their analysis performed according to the delocalization index (DI). In the Na5Li1 system, the atomic pairs Na1-Li2 and Na1-Li6 have the strongest interactions (equivalent to the NaLi system) of all Na-Li pairs in all of the NaxLiy (x+y=6) clusters; concurrently, other Na-Li pairs bear interactions ten times weaker than those from the NaLi system. The Na-Na interactions from the clusters Na4Li2 e Na5Li1 are stronger when compared to pure systems. Finally, it has been verified that the degree of degeneracy formula of the aromaticity index D3BIA and the atomic charge suggest that the lithium atoms that are closer to the sodium atom transfer charge to the latter.