Estudo teórico e análise do crescimento de clusters de sódio-potássio por algoritmo genético e cálculos de química quântica

Abstract

Particle aggregates which properties, at nanometric scale, embrace from those presented by its individual atoms or molecules to those presented at the bulk limit are referred to as clusters. These compounds may be considered as a relatively new type of material and are currently a frequent subject among scientific researches. The potential energy hypersurface associated with sodium-potassium alloy clusters, generated by the empirical Gupta expression, is explored via a modified genetic algorithm, enhanced by the addition of two different operators to the standard evolutionary procedure. Such classical approach is intended to provide, for the smaller clusters (up to 10 atoms), initial conditions for electronic structure methods. The minima of such empirical potential are assessed and corrected using high levei ab ínítío methods such as CCSD(T), CR-CCSD(T)-L and MP2, and benchmark results are obtained for specific cases. The results are the first calculations for such small alloy clusters and may serve as reference for further studies. The validity and choice of a proper functional and basis set for DFT calculations are then explored using the benchmark data, where it was found that the usual DFT approach may fail to provide the correct qualitative result for specific systems. The best general agreement to the benchmark calculations is achieved with def2-TZVPP basis set and SVWN5 functional, although the LANL2DZ basis set (with effective core potential) and SVWN5 functional provided the most cost-effective results. From this quantum approach, an insight is provided on the lower limits of applicability of the empirical Gupta potential, and thus the classical approach is proceeded to the larger clusters, up to the well-established 55 atoms structure, being their second-order energy difference and excess energies calculated. It is found that the most stable alloys (compared to the homonuclear counterparts) are achieved with the proportion of sodium atoms in the range of 30 to 40 %. The experimental propensity of core-shell segregation is successfully predicted by the current approach. Last but not least, the coupling between the efficient genetic algorithm, based on a new crossover routine, and the BFGS minimization technique implemented on GAMESS-US is pursued in order to provide an efficient methodology capable of generating good initial conditions for subsequent more rigorous evaluation through more robust techniques.