Numerical Analysis of the Results of Calculations of the Equilibrium Configuration of Silver Nanocrystals in the Framework of the Classical Sutton-Chen Mathematical Model and in the Quantum Pseudopotential Approximation of the Density Functional Theory

Abstract

In the present work, a comparative numerical analysis of the classical model of the Sutton-Chen interatomic interaction and a non-empirical quantum model was carried out within the framework of the theory of density functional (DFT) to calculate the equilibrium geometry of the nanocrystal Ag₁₄. A variant of DFP with a non-empirical pseudo-potential HW (Hay, Wadt) and an exchange-correlation function B3LYP (Becke, three-parameter, Lee-Yang-Parr) was used. The above models contained the equilibrium spatial configurations of this nanocrystal. To compare the results obtained, the coordinates of the atoms with respect to the center of mass of each relaxed nanocrystal were calculated. These coordinates were used to calculate a function that allows you to judge the distances of the nearest and subsequent atoms relative to the centers of mass of nanocrystals. The results are presented in graphical and tabular form. It turned out that atoms whose equilibrium positions are calculated within the framework of the Satton-Chen semi-empirical model are about 10% closer to the center of mass than in the non-empirical quantum model. Thus, the simple semi-empirical Satton-Chen model allows us to obtain quite reasonable data on the equilibrium coordinates of atoms in silver nanostructures. In addition, the machine time of calculations using the Satton-Chen mathematical model compared to quantum mechanical calculations is relatively small. Therefore, the application of the considered semi-empirical model to numerical modeling of the topology of silver nano systems with a complex spatial structure, in particular, containing edge dislocations, atomic rough surfaces, etc., is advisable and capable of obtaining correct results, at least at a qualitative level.