Increasing the efficiency of modeling the energy characteristics of nanoclusters

Context. The paper presents a computational scheme and a number of techniques for increasing the e(cid:30)ciency of mathematical modeling of the energy characteristics of metal clusters with vacancies. The object of the research is the process of calculating wave functions and (cid:28)nding eigenvalues using the Numerov and the shooting methods. local density approximation for calculating the energy characteristics of nanoclusters. At the simulation stage, the one-electron wave function was calculated by (cid:16)stitching(cid:17) it from two parts at an empirically selected point with normalization before and after the procedure. A number of techniques have been developed to improve the quality of the simulation: calculating the optimal step, limiting changes in the electrostatic pro(cid:28)le, managing the resulting data arrays, etc. For calculations on a supercomputer, the distribution between the (cid:29)ows was carried out. Results. At the modeling stage, economic models of the metal sphere with a vacancy in the center were developed. For the simulation stage, a method of stable two-sided calculation of the wave function using the shooting and the Numerov methods with the optimal step has been developed. The full computational scheme for the simulation is implemented in C ++ for calculation on a PC and on a supercomputer. The simulation results were compared with the ab-initio calculation data and experimental data for Cs, Rb, K, Na, Li, Mg, and Al clusters with and without vacancies (calculation error < 15%). Conclusions. The developed computational scheme and modeling technique allow increasing the simulation e(cid:30)ciency and obtaining adequate energy characteristics of metal spherical nanoclusters with and without vacancies. Further research might focus on the modi(cid:28)cation of models and simulation techniques for the study of layered nanoscale systems.