The electron density distribution function for metallic nanoparticles within the framework of the theory of density functionals
Authors: Fedorova V.Yu.  
Published in issue: #8(25)/2018  
DOI: 10.18698/2541800920188355  
Category: Physics  Chapter: Physics and technology of nanostructures, nuclear and molecular 

Keywords: density functional method, nanopowder, jelly model, electron density, variational method, Friedel oscillations, Schrödinger equation, potential well 

Published: 07.08.2018 
The paper presents the choice of the trial electron density function in the framework of the density functional theory for the jelly model describing a system consisting of spherically symmetric aluminum nanoparticles. The effect that occurs near the metalenvironment boundary associated with Friedel oscillations is taken into account. The conditions for the possibility of using a given function for further calculations of the surface energy, work function, and other characteristics of the nanopowder of a given metal are set. Within the framework of the variational method, numerical calculations of the necessary coefficients and variational parameters for different radii of nanoparticles are given, taking into account the average electron density of aluminum used for subsequent calculations of energy characteristics.
References
[1] Kohn V. Electron material structure – wave functions and density functional. UFN, 2002, vol. 172, no. 3, pp. 336–348.
[2] Partenskiy M.B. Selfconsistent electron theory of a metallic surface. UFN, 1979, vol. 128, no. 5, pp. 69–106. (Eng. version: Sov. Phys. Usp., 1979, vol. 22, no. 3, pp. 330–351.)
[3] Satanin A.M. Vvedenie v teoriyu funktsionala plotnosti [Introduction to density functional theory]. Nizhniy Novgorod, UNN publ., 2009, 64 p.
[4] Smith J.R. Selfconsistent manyelectron theory of electron work functions and surface potential characteristics for selected metals. Physical Review, 1969, vol. 181, no. 2, pp. 522–529.
[5] Kiejna A., Wojciechowski K.F. Metal surface electron physics. Pergamon, 1996, 312 p.
[6] Sarkisov P.D., Baykov Yu.A., Meshalkin V.P. Selfconsisted field method in Hartree approximation of twoelectron systems for different electron configurations. Doklady akademii nauk, 2008, vol. 423, no. 3, pp. 331–335.
[7] Mayer I. Simple theorems, proofs and derivations in quantum chemistry. Springer, 2003, 337 p.
[8] Glushkov V.L., Erkovich O.S. Surface characteristics of alkali metals with the discrete lattice and Friedel oscillations of the electron density. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2017, no. 4, pp. 75–89.
[9] Mamonova M.V., Bartysheva M.A. Description of the influence of the Friedel oscillations in the calculation of the distribution of electron density and the surface energy of metals. Vestnik Omskogo universiteta [Herald of Omsk University], 2010, no. 2, pp. 39–43.
[10] Chaplik A.V., Kovalev V.M., Magarill L.I., Vitlina R.Z. Electrostatic screening and Friedel oscillations in nanostructures. Journal of superconductivity and novel magnetism, 2012, vol. 25, no. 3, pp. 699–709.