Simulation of Spherical Metal Nanoclusters Containing Monovacancy

Authors V.I. Reva , O.V. Vasylenko, V.V. Pogosov

National University Zaporizka Politekhnika, 64, Zhukovsky St., 69063 Zaporizhzhya, Ukraine

Issue Volume 11, Year 2019, Number 5
Dates Received 27 April 2019; revised manuscript received 21 October 2019; published online 25 October 2019
Citation V.I. Reva, O.V. Vasylenko, V.V. Pogosov, J. Nano- Electron. Phys. 11 No 5, 05018 (2019)
PACS Number(s) 02.60.Cb, 31.15.Es
Keywords Metal clusters, Energy characteristics, DFT (32) , Wave function, Numerov method, "Cross-linking" of functions, Stability of the simulation.

The goal of this work was to increase the stability of the simulation based on the Numerov method during the calculation of the electron wave functions in a metal cluster and to ensure the stability of self-consistent calculations of the energy characteristics of metal clusters by limitation of the electrostatic potential changes. The object of the study is the method for calculation of the electron wave functions and energy eigenvalues by the Numerov and Shooting methods. At the modeling stage, in order to increase the efficiency of the model, the density functional theory (DFT) was used in conjunction with the Kohn-Shem formalism, which allowed us to simplify the complex problem of the electron interaction in the field of charged ions and to obtain the model of independent electrons moving in some effective potential. We used the stabilized jellium model (SJM) and local density approximation (LDA) for the exchange and correlation energies. The change of the electrostatic potential profile limitation is used by adding coefficients that determine the contributions of the previous and current electrostatic potential profile to the resultant one. Models of a metal cluster with a centered monovacancy and approaches for calculating its parameters were developed. To ensure the convergence and stability of the Numerov method, methods of two-side calculation with "cross-linking" of the wave function at the empirically selected point were proposed. The method of simulation with the optimal step is developed and implemented in the program code for calculating the energy characteristics of metal nanoclusters containing the monovacancy. Simulation allowed to obtain the electron density and effective potential profiles for charged and neutral clusters. The results of the calculations were compared with experimental data, as well as with ab initio computations. Developed approaches and simulation techniques can be recommended for the analysis of low-dimensional metal systems, including systems with a layered structure.

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