Aplicação de algoritmos genéticos: determinação de estruturas de clusters atômicos e liberação controlada de sistemas farmacêuticos

Abstract

Atomic structure prediction of materials is of much interest, especially for atomic clusters since they show different physical and chemical properties when compared to their bulk counterpart. Knowledge of their structural change as function of size may lead to the discovery of new nanostructured materials with interesting technological applications. Thestructure determination of atomic clusters directly from experiments is still rather limited, but some progress can be made upon comparison of the experimental data with theoretical modelling. The major goal of this work is to explore the potential energy surfaces of atomic clusters using genetic algorithms to find the most stable structures. In the first part of thethesis we introduce a method based on pre-screening with follow-up structure refinement: the potential energy surface is first sampled at an interatomic potential level, then the candidate structures are further reoptimized at the density functional theory (DFT) level. Two different ab-initio computational techniques are used: the real-space DFT calculation, using high-order finite differences and atomic pseudopotentials, and the DFT method based on Gaussian basis set. We applied the method in the structure determination of carbonclusters as function of cluster size (3 25 atoms). As the cluster size increases, topological changes emerge, ranging from linear chains and polyciclic graphene-like structures to fullerenes. We also determined and compared the electronic and vibrational properties of the carbon clusters with the two DFT techniques. In the second part of the thesiswe follow a different strategy for energy surface exploration, using the direct coupling of the genetic algorithm with electronic structure methods, bypassing completely the use of interatomic potentials. We investigated the structural properties of bimetallic alkali nanoalloys of sodium potassium as function of cluster size (4 9 atoms) with a simplified version of our original genetic algorithm where the individuals of the population are geometrically relaxed at the second-order Möller-Plesset perturbation theory, with effective core potential (MP2/ECP), and DFT theory levels. We confirm the previous theoretical identification of composition segregation in alkali clusters, specifically, in ourcase study, with the potassium atoms migrating to the surface of the clusters and the core regions preferably occupied by sodium atoms. We make a detailed analysis of the 2D3D2D morphological transition as function of composition for clusters with a total of six atoms. For larger clusters new structures are determined. The final part of the thesisconcerns the applicability of the genetic algorithm framework as a complementary tool for the development and formulation of controlled release pharmaceutical dosage forms. We specifically propose to use a mathematical model that best describes the drug release profile from a polymeric device to get, by inversion, the initial formulation parameters,such as the composition, device geometry and drug loading. We formulate the inverse problem in terms of an optimization problem for finding multiple solutions. Our aim is to offer a large data set of candidate device configurations for a targeted drug release profile to improve the systematic Design of Experiments (DoE).